1
|
Spike-induced ordering: Stochastic neural spikes provide immediate adaptability to the sensorimotor system. Proc Natl Acad Sci U S A 2020; 117:12486-12496. [PMID: 32430332 PMCID: PMC7275765 DOI: 10.1073/pnas.1819707117] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The functional advantages of using a stochastically spiking neural network (sSNN) instead of a nonspiking neural network (NS-NN) have remained largely unknown. We developed an architecture which enabled the parametric adjustment of the spikiness (i.e., impulsive dynamics and stochasticity) of the sSNN output and observed that stochastic spikes instantaneously induced the ordered motion of a dynamical system. We demonstrated the benefits of sSNNs using a musculoskeletal bipedal walker and, moreover, showed that the decrease in the spikiness of motor neuron output leads to a reduction in adaptability. Stochastic spikes may aid the adaptation of a biological system to sudden perturbations or environmental changes. Our architecture can easily be connected to the conventional NS-NN and may superimpose the on-site adaptability. Most biological neurons exhibit stochastic and spiking action potentials. However, the benefits of stochastic spikes versus continuous signals other than noise tolerance and energy efficiency remain largely unknown. In this study, we provide an insight into the potential roles of stochastic spikes, which may be beneficial for producing on-site adaptability in biological sensorimotor agents. We developed a platform that enables parametric modulation of the stochastic and discontinuous output of a stochastically spiking neural network (sSNN) to the rate-coded smooth output. This platform was applied to a complex musculoskeletal–neural system of a bipedal walker, and we demonstrated how stochastic spikes may help improve on-site adaptability of a bipedal walker to slippery surfaces or perturbation of random external forces. We further applied our sSNN platform to more general and simple sensorimotor agents and demonstrated four basic functions provided by an sSNN: 1) synchronization to a natural frequency, 2) amplification of the resonant motion in a natural frequency, 3) basin enlargement of the behavioral goal state, and 4) rapid complexity reduction and regular motion pattern formation. We propose that the benefits of sSNNs are not limited to musculoskeletal dynamics. Indeed, a wide range of the stability and adaptability of biological systems may arise from stochastic spiking dynamics.
Collapse
|
2
|
Buceta J. Finite cell-size effects on protein variability in Turing patterned tissues. J R Soc Interface 2017; 14:20170316. [PMID: 28855385 PMCID: PMC5582127 DOI: 10.1098/rsif.2017.0316] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2017] [Accepted: 08/02/2017] [Indexed: 01/20/2023] Open
Abstract
Herein we present a framework to characterize different sources of protein expression variability in Turing patterned tissues. In this context, we introduce the concept of granular noise to account for the unavoidable fluctuations due to finite cell-size effects and show that the nearest-neighbours autocorrelation function provides the means to measure it. To test our findings, we perform in silico experiments of growing tissues driven by a generic activator-inhibitor dynamics. Our results show that the relative importance of different sources of noise depends on the ratio between the characteristic size of cells and that of the pattern domains and on the ratio between the pattern amplitude and the effective intensity of the biochemical fluctuations. Importantly, our framework provides the tools to measure and distinguish different stochastic contributions during patterning: granularity versus biochemical noise. In addition, our analysis identifies the protein species that buffer the stochasticity the best and, consequently, it can help to determine key instructive signals in systems driven by a Turing instability. Altogether, we expect our study to be relevant in developmental processes leading to the formation of periodic patterns in tissues.
Collapse
Affiliation(s)
- Javier Buceta
- Department of Bioengineering, Lehigh University, Iacocca Hall, 111 Research Drive, Bethlehem, PA 18015, USA
- Department of Chemical and Biomolecular Engineering, Lehigh University, Iacocca Hall, 111 Research Drive, Bethlehem, PA 18015, USA
| |
Collapse
|
3
|
Zarza GA, Mangioni SE, Acevedo JF, Deza RR. Limiting the stroke of a Schmitt trigger with multiplicative noise. Phys Rev E 2017; 95:052143. [PMID: 28618519 DOI: 10.1103/physreve.95.052143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2016] [Indexed: 11/07/2022]
Abstract
We have devised an experiment whereby a bistable system is confined away from its deterministic attractors by means of multiplicative noise. Together with previous numerical results, our experimental results validate the hypothesis that the higher the slope of the noise's multiplicative factor, the more it shifts the stationary states.
Collapse
Affiliation(s)
- Gabriel A Zarza
- IFIMAR (Universidad Nacional de Mar del Plata and CONICET), Deán Funes 3350, B7602AYL Mar del Plata, Argentina
| | - Sergio E Mangioni
- IFIMAR (Universidad Nacional de Mar del Plata and CONICET), Deán Funes 3350, B7602AYL Mar del Plata, Argentina
| | - Javier Fernandez Acevedo
- IFIMAR (Universidad Nacional de Mar del Plata and CONICET), Deán Funes 3350, B7602AYL Mar del Plata, Argentina
| | - Roberto R Deza
- IFIMAR (Universidad Nacional de Mar del Plata and CONICET), Deán Funes 3350, B7602AYL Mar del Plata, Argentina
| |
Collapse
|
4
|
Paul S, Ghosh S, Ray DS. Noisy-flow-induced instability in a reaction-diffusion system. Phys Rev E 2017; 94:062217. [PMID: 28085378 DOI: 10.1103/physreve.94.062217] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Indexed: 11/07/2022]
Abstract
We consider a generic reaction-diffusion-advection system where the flow velocity of the advection term is subjected to dichotomous noise with zero mean and Ornstein-Zernike correlation. A general condition for noisy-flow-induced instability is derived in the flow velocity-correlation rate parameter plane. Full numerical simulations on Gierer-Meinhardt model with activator-inhibitor kinetics have been performed to show how noisy differential flow can lead to symmetry breaking of a homogeneous stable state in the presence of noise resulting in traveling waves.
Collapse
Affiliation(s)
- Shibashis Paul
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Shyamolina Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| |
Collapse
|
5
|
Mangioni SE. Cooperation between fluctuations and spatial coupling for two symmetry breakings in a gradient system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062136. [PMID: 26764661 DOI: 10.1103/physreve.92.062136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2015] [Indexed: 06/05/2023]
Abstract
A zero-dimensional system that is affected by field-dependent fluctuations evolves toward the field's values in which the fluctuations' effect is minimized. For a high enough noise intensity, it causes an exchange of roles between the stable and unstable state. In this paper, we report symmetry breaking in two stable states, but one of them stabilized by the fluctuations while exchanging its role with a previously stable state.
Collapse
Affiliation(s)
- Sergio E Mangioni
- IFIMAR (Universidad Nacional de Mar del Plata and CONICET), and Deán Funes 3350, B7602AYL Mar del Plata, Argentina
| |
Collapse
|
6
|
Samanta HS, Bhattacharjee JK, Bhattacharyay A, Chakraborty S. On noise induced Poincaré-Andronov-Hopf bifurcation. CHAOS (WOODBURY, N.Y.) 2014; 24:043122. [PMID: 25554042 DOI: 10.1063/1.4900775] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
It has been numerically seen that noise introduces stable well-defined oscillatory state in a system with unstable limit cycles resulting from subcritical Poincaré-Andronov-Hopf (or simply Hopf) bifurcation. This phenomenon is analogous to the well known stochastic resonance in the sense that it effectively converts noise into useful energy. Herein, we clearly explain how noise induced imperfection in the bifurcation is a generic reason for such a phenomenon to occur and provide explicit analytical calculations in order to explain the typical square-root dependence of the oscillations' amplitude on the noise level below a certain threshold value. Also, we argue that the noise can bring forth oscillations in average sense even in the absence of a limit cycle. Thus, we bring forward the inherent general mechanism of the noise induced Hopf bifurcation naturally realisable across disciplines.
Collapse
Affiliation(s)
- Himadri S Samanta
- Biophysics Program, Institute For Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | | | | | - Sagar Chakraborty
- Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
| |
Collapse
|
7
|
Tang Y, Yuan R, Chen J, Ao P. Controlling symmetry-breaking states by a hidden quantity in multiplicative noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052121. [PMID: 25493754 DOI: 10.1103/physreve.90.052121] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2014] [Indexed: 06/04/2023]
Abstract
The inhomogeneity of multiplicative white noise leads to various coupling modes between deterministic and stochastic forces. We investigate the phase transition induced by the variation of the coupling mode through manipulating its characteristic parameter continuously. Even when the noise strength is fixed, an increase of this parameter can enhance or inhibit the symmetry-breaking state. We also propose a scheme to implement these phase transitions experimentally. Our result demonstrates that the coupling mode previously considered to be a mathematical convention serves as an additional quantity leading to physically observable phase transitions. This observation provides a mechanism to control the effect of noise without regulating the noise strength.
Collapse
Affiliation(s)
- Ying Tang
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China and Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ruoshi Yuan
- School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Jianhong Chen
- ZhiYuan College, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ping Ao
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China and Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
| |
Collapse
|
8
|
Kurushina SE, Maximov VV, Romanovskii YM. Weiss mean-field approximation for multicomponent stochastic spatially extended systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022135. [PMID: 25215716 DOI: 10.1103/physreve.90.022135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2014] [Indexed: 06/03/2023]
Abstract
We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system, which describes a well-known model of autocatalytic chemical reaction (brusselator) with spatially correlated multiplicative noise, and to study the evolution of probability density and statistical characteristics of the system in the process of spatial pattern formation. We propose the finite-difference method for the numerical solving of a general class of multivariate nonlinear self-consistent time-dependent Fokker-Planck equations. We illustrate the accuracy and reliability of the method by applying it to an exactly solvable nonlinear Fokker-Planck equation (NFPE) for the Shimizu-Yamada model [Prog. Theor. Phys. 47, 350 (1972)] and nonlinear Fokker-Planck equation [Desai and Zwanzig, J. Stat. Phys. 19, 1 (1978)] obtained for a nonlinear stochastic mean-field model introduced by Kometani and Shimizu [J. Stat. Phys. 13, 473 (1975)]. Taking the problems indicated above as an example, the accuracy of the method is compared with the accuracy of Hermite distributed approximating functional method [Zhang et al., Phys. Rev. E 56, 1197 (1997)]. Numerical study of the NFPE solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple "repumping" of probability density through bimodality. Additionally, we study the behavior of the order parameter of the system under consideration and show that the second type of solution arises in the supercritical region if noise intensity values are close to the values appropriate for the transition from bimodal stationary probability density for the order parameter to the unimodal one.
Collapse
Affiliation(s)
- Svetlana E Kurushina
- Physics Department, Samara State Aerospace University named after S.P. Korolyov, Moskovskoye Shosse 34, 443086 Samara, Russian Federation, and Mathematics Department, Samara State Transport University, First Bezimyannii Pereulok 18, 443066 Samara, Russian Federation
| | - Valerii V Maximov
- Physics Department, Samara State Aerospace University named after S.P. Korolyov, Moskovskoye Shosse 34, 443086 Samara, Russian Federation, and Mathematics Department, Samara State Transport University, First Bezimyannii Pereulok 18, 443066 Samara, Russian Federation
| | - Yurii M Romanovskii
- Physics Department, Lomonosov Moscow State University, GSP-1, Leninskie Gory, 119991 Moscow, Russian Federation
| |
Collapse
|
9
|
Ghosh S, Ray DS. Nonlinear vibrational resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042904. [PMID: 24229246 DOI: 10.1103/physreve.88.042904] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2013] [Indexed: 06/02/2023]
Abstract
We examine the nonlinear response of a bistable system driven by a high-frequency force to a low-frequency weak field. It is shown that the rapidly varying temporal oscillation breaks the spatial symmetry of the centrosymmetric potential. This gives rise to a finite nonzero response at the second harmonic of the low-frequency field, which can be optimized by an appropriate choice of vibrational amplitude of the high-frequency field close to that for the linear response. The potential implications of the nonlinear vibrational resonance are analyzed.
Collapse
Affiliation(s)
- Shyamolina Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | | |
Collapse
|
10
|
Das D, Ray DS. Dichotomous-noise-induced pattern formation in a reaction-diffusion system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062924. [PMID: 23848765 DOI: 10.1103/physreve.87.062924] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2013] [Revised: 04/24/2013] [Indexed: 06/02/2023]
Abstract
We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.
Collapse
Affiliation(s)
- Debojyoti Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | | |
Collapse
|
11
|
Noise-induced spatiotemporal patterns in Hodgkin-Huxley neuronal network. Cogn Neurodyn 2013; 7:431-40. [PMID: 24427217 DOI: 10.1007/s11571-013-9245-1] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2012] [Revised: 01/21/2013] [Accepted: 01/23/2013] [Indexed: 10/27/2022] Open
Abstract
The effect of noise on the pattern selection in a regular network of Hodgkin-Huxley neurons is investigated, and the transition of pattern in the network is measured from subexcitable to excitable media. Extensive numerical results confirm that kinds of travelling wave such as spiral wave, circle wave and target wave could be developed and kept alive in the subexcitable network due to the noise. In the case of excitable media under noise, the developed spiral wave and target wave could coexist and new target-like wave is induced near to the border of media. The averaged membrane potentials over all neurons in the network are calculated to detect the periodicity of the time series and the generated traveling wave. Furthermore, the firing probabilities of neurons in networks are also calculated to analyze the collective behavior of networks.
Collapse
|
12
|
Kurushina SE, Maximov VV, Romanovskii YM. Spatial pattern formation in external noise: theory and simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011124. [PMID: 23005385 DOI: 10.1103/physreve.86.011124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2012] [Revised: 04/12/2012] [Indexed: 06/01/2023]
Abstract
Spatial pattern formation in fluctuating media is researched analytically from the point of view of the order parameters concept. A reaction-diffusion system with external noise is considered as a model of such media. Stochastic equations for unstable mode amplitudes (order parameters), the dispersion equation for averaged amplitudes of unstable modes, and the Fokker-Planck equation for the order parameters are obtained. The theory developed makes it possible to analyze different noise-induced effects including the variation of boundaries of ordering and disordering phase transitions depending on the parameters of external noise.
Collapse
Affiliation(s)
- S E Kurushina
- Physics Department, Samara State Aerospace University, Moskovskoye Shosse 34, Samara 443086, Russian Federation.
| | | | | |
Collapse
|
13
|
Mangioni SE, Deza RR. Nonequilibrium pattern formation by subdominant attractive forces: a simple model and a stabilization strategy by means of noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:042101. [PMID: 21230330 DOI: 10.1103/physreve.82.042101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2010] [Indexed: 05/30/2023]
Abstract
We introduce a simple model describing a mechanism for transient pattern formation driven by subdominant attractive forces. The patterns can be stabilized if they are confined by means of a particular multiplicative noise into the region where such mechanism is active. The scope of the results appears to transcend the original application context.
Collapse
Affiliation(s)
- Sergio E Mangioni
- IFIMAR, UNMdP-CONICET, Deán Funes 3350, B7602AYL Mar del Plata, Argentina
| | | |
Collapse
|
14
|
Baura A, Sen MK, Bag BC. Magnetic-field-induced breakdown of equivalence of multidimensional motion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041102. [PMID: 21230233 DOI: 10.1103/physreve.82.041102] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2010] [Revised: 06/27/2010] [Indexed: 05/30/2023]
Abstract
In this paper, we have studied Brownian motion in multidimension phase space in presence of a magnetic field. The nonequilibrium behavior of thermodynamically inspired quantities along the individual component of motion has been studied in detail. Based on the Fokker-Planck description of the stochastic process and entropy balance equation, we have calculated information entropy production and entropy flux at nonequilibrium state. The dependence of these quantities on time, magnetic field, and thermal bath is studied. In this context, we have observed that there exists extremum behavior in the dynamics and the applied magnetic field breaks the equivalence in motion of the components in the nonequilibrium state.
Collapse
Affiliation(s)
- Alendu Baura
- Department of Chemistry, Visva-Bharati, Santiniketan 731 235, India
| | | | | |
Collapse
|
15
|
Lu X, Wang C, Qiao C, Wu Y, Ouyang Q, Wang H. Effect of noise on chemical waves in three-dimensional reaction-diffusion systems with gradient. J Chem Phys 2008; 128:114505. [DOI: 10.1063/1.2894473] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
16
|
Riaz SS, Sharma R, Bhattacharyya SP, Ray DS. Instability and pattern formation in reaction-diffusion systems: A higher order analysis. J Chem Phys 2007; 127:064503. [PMID: 17705608 DOI: 10.1063/1.2759212] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We analyze the condition for instability and pattern formation in reaction-diffusion systems beyond the usual linear regime. The approach is based on taking into account perturbations of higher orders. Our analysis reveals that nonlinearity present in the system can be instrumental in determining the stability of a system, even to the extent of destabilizing one in a linearly stable parameter regime. The analysis is also successful to account for the observed effect of additive noise in modifying the instability threshold of a system. The analytical study is corroborated by numerical simulation in a standard reaction-diffusion system.
Collapse
Affiliation(s)
- Syed Shahed Riaz
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | | | | | | |
Collapse
|
17
|
Wang H, Fu Z, Xu X, Ouyang Q. Pattern Formation Induced by Internal Microscopic Fluctuations. J Phys Chem A 2007; 111:1265-70. [PMID: 17256832 DOI: 10.1021/jp0674064] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report spatiotemporal patterns induced by microscopic fluctuations in the Gray-Scott model. In the framework of stochastic kinetics, the macroscopic effect of internal noise of the system was investigated by simulating the reaction-diffusion master equation using Gillespie's algorithm. Pattern formation at the level of stochastic description is presented in comparison with that given by deterministic equations. Complex spatiotemporal patterns, including spiral waves, Turing patterns, self-replicating spots and others, which are not captured or correctly predicted by the deterministic reaction-diffusion equations, are induced by internal reaction fluctuations. Furthermore the intrinsic noise selects and controls the pattern formation with different intensities of fluctuation.
Collapse
Affiliation(s)
- Hongli Wang
- Department of Physics, and The Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (PKU), and Center for Theoretical Biology, Peking University, Beijing 100871, China
| | | | | | | |
Collapse
|
18
|
Wang H, Zhang K, Ouyang Q. Resonant-pattern formation induced by additive noise in periodically forced reaction-diffusion systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:036210. [PMID: 17025732 DOI: 10.1103/physreve.74.036210] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2006] [Revised: 08/16/2006] [Indexed: 05/12/2023]
Abstract
We report frequency-locked resonant patterns induced by additive noise in periodically forced reaction-diffusion Brusselator model. In the regime of 2:1 frequency-locking and homogeneous oscillation, the introduction of additive noise, which is colored in time and white in space, generates and sustains resonant patterns of hexagons, stripes, and labyrinths which oscillate at half of the forcing frequency. Both the noise strength and the correlation time control the pattern formation. The system transits from homogeneous to hexagons, stripes, and to labyrinths successively as the noise strength is adjusted. Good frequency-locked patterns are only sustained by the colored noise and a finite time correlation is necessary. At the limit of white noise with zero temporal correlation, irregular patterns which are only nearly resonant come out as the noise strength is adjusted. The phenomenon induced by colored noise in the forced reaction-diffusion system is demonstrated to correspond to noise-induced Turing instability in the corresponding forced complex Ginzburg-Landau equation.
Collapse
Affiliation(s)
- Hongli Wang
- Department of Physics, Peking University, Beijing 100871, People's Republic of China
| | | | | |
Collapse
|
19
|
Clerc MG, Falcón C, Tirapegui E. Front propagation sustained by additive noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011303. [PMID: 16907085 DOI: 10.1103/physreve.74.011303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2006] [Indexed: 05/11/2023]
Abstract
The effect of noise in a motionless front between a periodic spatial state and an homogeneous one is studied. Numerical simulations show that noise induces front propagation. From the subcritical Swift-Hohenberg equation with noise, we deduce an adequate equation for the envelope and the core of the front. The equation of the core of the front is characterized by an asymmetrical periodic potential plus additive noise. The conversion of random fluctuations into direct motion of the core of the front is responsible of the propagation. We obtain an analytical expression for the velocity of the front, which is in good agreement with numerical simulations.
Collapse
Affiliation(s)
- M G Clerc
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | | | | |
Collapse
|
20
|
Sailer X, Hennig D, Beato V, Engel H, Schimansky-Geier L. Regular patterns in dichotomically driven activator-inhibitor dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056209. [PMID: 16803028 DOI: 10.1103/physreve.73.056209] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2005] [Indexed: 05/10/2023]
Abstract
We investigate Turing pattern formation in the presence of additive dichotomous fluctuations in the context of an extended system with diffusive coupling and FitzHugh-Nagumo kinetics. The fluctuations vary in space and/or time. Depending on the realization of the dichotomous switching the system is, at a given time (for spatial disorder at a given position) in one of two possible excitable dynamical regimes. Each of the two excitable dynamics for itself does not support pattern formation. With proper dichotomous fluctuations, however, the homogeneous steady state is destabilized via a Turing instability. We investigate the influence of different switching rates (different correlation length of the spatial disorder) on pattern formation. We find three distinct mechanisms: For slow switching existing boundaries become unstable, for high rates the system exhibits "effective bistability" which allows for a Turing instability. For medium rates the fluctuations create spatial structures via a new mechanism where the influence of the fluctuations is twofold. First they produce local inhomogeneities, which then grow (again caused by fluctuations) until the whole space is covered. Utilizing a nonlinear map approach we show bistability of a period-one and a period-two orbit being associated with the steady homogeneous and the Turing pattern state, respectively. Finally, for purely static dichotomous disorder we find destabilization of homogeneous steady states for finite nonzero correlation length of the disorder resulting again in Turing patterns.
Collapse
Affiliation(s)
- X Sailer
- Institut für Physik, Humboldt-Universität zu Berlin, Germany
| | | | | | | | | |
Collapse
|
21
|
Buceta J, Wood K, Lindenberg K. Noise-induced oscillatory behavior in field-dependent relaxational dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:042101. [PMID: 16711860 DOI: 10.1103/physreve.73.042101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2005] [Revised: 02/08/2006] [Indexed: 05/09/2023]
Abstract
By considering inertial effects in a field-dependent relaxational model, we show that noise may induce collective oscillatory dynamics. In agreement with the recently introduced idea of noise-induced multistability, we show that there is a region in parameter space where such behavior depends on the initial condition. Moreover, when the coupling term leads to pattern formation by means of a morphological instability a la Swift-Hohenberg, [J. Buceta, M. Ibañes, J. M. Sancho, and K. Lindenberg, Phys. Rev. E 67, 021113 (2003) and K. Wood, J. Buceta, and K. Lindenberg, Phys. Rev. E 73, 022101 (2006)] our numerical simulations reveal that spatio-temporal oscillatory structures develop.
Collapse
Affiliation(s)
- J Buceta
- Parc Científic de Barcelona, Centre de Recerca en Química Teórica (CeRQT), Campus Diagonal-Universitat de Barcelona, Edifici Modular, C/Josep Samitier 1-5, 08028 Barcelona, Spain
| | | | | |
Collapse
|
22
|
Wood K, Buceta J, Lindenberg K. Comprehensive study of pattern formation in relaxational systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:022101. [PMID: 16605372 DOI: 10.1103/physreve.73.022101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2005] [Indexed: 05/08/2023]
Abstract
We present a comprehensive study of pattern formation in single-field relaxational systems with field-dependent coefficients. A modulated mean-field theory leads to a form amenable to analysis via the geometric architecture developed in our earlier work for systems that exhibit phase transitions between global steady states [Phys. Rev. E 69, 011102 (2004)]. We demonstrate that the phase diagrams for these systems are entirely determined by a few geometric properties of the field-dependent relaxational coefficient and the local potential. Numerical simulations support the theoretical predictions.
Collapse
Affiliation(s)
- Kevin Wood
- Department of Chemistry and Biochemistry 0340, and Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
| | | | | |
Collapse
|
23
|
Ghosh PK, Barik D, Bag BC, Ray DS. Quantum escape kinetics over a fluctuating barrier. J Chem Phys 2005; 123:224104. [PMID: 16375467 DOI: 10.1063/1.2135781] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The escape rate of a particle over a fluctuating barrier in a double-well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of chemical reactions. We extend the analysis of this phenomenon of resonant activation to quantum domain to show how quantization significantly enhances resonant activation at low temperature due to tunneling.
Collapse
Affiliation(s)
- Pulak Kumar Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | | | | | | |
Collapse
|
24
|
Clerc MG, Falcon C, Tirapegui E. Additive noise induces front propagation. PHYSICAL REVIEW LETTERS 2005; 94:148302. [PMID: 15904121 DOI: 10.1103/physrevlett.94.148302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2004] [Indexed: 05/02/2023]
Abstract
The effect of additive noise on a static front that connects a stable homogeneous state with an also stable but spatially periodic state is studied. Numerical simulations show that noise induces front propagation. The conversion of random fluctuations into direct motion of the front's core is responsible of the propagation; noise prefers to create or remove a bump, because the necessary perturbations to nucleate or destroy a bump are different. From a prototype model with noise, we deduce an adequate equation for the front's core. An analytical expression for the front velocity is deduced, which is in good agreement with numerical simulations.
Collapse
Affiliation(s)
- M G Clerc
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | | | | |
Collapse
|
25
|
Kawai R, Sailer X, Schimansky-Geier L, Van den Broeck C. Macroscopic limit cycle via pure noise-induced phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:051104. [PMID: 15244805 DOI: 10.1103/physreve.69.051104] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2003] [Indexed: 05/24/2023]
Abstract
Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an analytical study of the phase diagram in more general cases than previous methods. In addition, using this approach we investigate spatially extended systems with two degrees of freedom per site. For this system, the analytic solution of the stationary Fokker-Planck equation is not available and a standard mean field approach cannot be used to find noise-induced phase transitions. A different approach based on cumulant dynamics predicts a noise-induced phase transition through a Hopf bifurcation leading to a macroscopic limit cycle motion, which is confirmed by numerical simulation.
Collapse
Affiliation(s)
- R Kawai
- Department of Physics, University of Alabama at Birmingham, 1300 University Boulevard, Birmingham, Alabama 35294, USA.
| | | | | | | |
Collapse
|
26
|
Buceta J, Lindenberg K. Comprehensive study of phase transitions in relaxational systems with field-dependent coefficients. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:011102. [PMID: 14995599 DOI: 10.1103/physreve.69.011102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2003] [Indexed: 05/24/2023]
Abstract
We present a comprehensive study of phase transitions in single-field systems that relax to a nonequilibrium global steady state. The mechanism we focus on is not the so-called Stratonovich drift combined with collective effects, but is instead similar to the one associated with noise-induced transitions in the manner of Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise interpretation (e.g., Itô vs Stratonovich) merely shifts the phase boundaries. With the help of a mean-field approximation, we present a broad qualitative picture of the various phase diagrams that can be found in these systems. To complement the theoretical analysis we present numerical simulations that confirm the findings of the mean-field theory.
Collapse
Affiliation(s)
- J Buceta
- Department of Chemistry and Biochemistry, and Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, USA
| | | |
Collapse
|
27
|
Buceta J, Lindenberg K. Spatial patterns induced purely by dichotomous disorder. PHYSICAL REVIEW E 2003; 68:011103. [PMID: 12935123 DOI: 10.1103/physreve.68.011103] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2003] [Indexed: 11/07/2022]
Abstract
We study conditions under which spatially extended systems with coupling in the manner of Swift and Hohenberg exhibit spatial patterns induced purely by the presence of quenched dichotomous disorder. Complementing the theoretical results based on a generalized mean-field approximation, we also present numerical simulations of particular dynamical systems that exhibit the proposed phenomenology.
Collapse
Affiliation(s)
- J Buceta
- Department of Chemistry and Biochemistry, and Institute for Nonlinear Science, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, USA
| | | |
Collapse
|
28
|
Carrillo O, Ibañes M, García-Ojalvo J, Casademunt J, Sancho JM. Intrinsic noise-induced phase transitions: beyond the noise interpretation. PHYSICAL REVIEW E 2003; 67:046110. [PMID: 12786439 DOI: 10.1103/physreve.67.046110] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2002] [Indexed: 11/07/2022]
Abstract
We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Itô vs Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Itô. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau-type model. A detailed discussion of a different numerical algorithm valid for both interpretations is also presented.
Collapse
Affiliation(s)
- O Carrillo
- Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
| | | | | | | | | |
Collapse
|