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Kumar P, Gangopadhyay G. Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions. Chemphyschem 2023; 24:e202200643. [PMID: 36478341 DOI: 10.1002/cphc.202200643] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Revised: 11/21/2022] [Indexed: 12/12/2022]
Abstract
An inhomogeneous profile of chemostatted species generates a rich variety of patterns in glycolytic waves depicted in a Selkov reaction-diffusion framework here. A key role played by diffusion amplitude and symmetry in the chemostatted species profile in dictating the fate of local spatial dynamics involving periodic, quasiperiodic, and chaotic patterns and transitions among them are investigated systematically. More importantly, various dynamic transitions, including wave propagation direction changes, are illustrated in interesting situations. Besides numerical results, our analytical formulation of the amplitude equation connecting complex Ginzburg-Landau and Lambda-omega representation shed light on the phase dynamics of the system. This systematic study of the glycolytic reaction-diffusion wave is in line with previous experimental results in open spatial reactor and will provide a knowledge about the dynamics that shape and control biological information processing and related phenomena.
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Affiliation(s)
- Premashis Kumar
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata, 700 106, India
| | - Gautam Gangopadhyay
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata, 700 106, India
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2
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Sato M, Hyodo H, Biwa T, Delage R. Synchronization of thermoacoustic quasiperiodic oscillation by periodic external force. CHAOS (WOODBURY, N.Y.) 2020; 30:063130. [PMID: 32611130 DOI: 10.1063/5.0004381] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Accepted: 05/22/2020] [Indexed: 06/11/2023]
Abstract
Quasiperiodic oscillations can occur in nonequilibrium systems where two or more frequency components are generated simultaneously. Many studies have explored the synchronization of periodic and chaotic oscillations; however, the synchronization of quasiperiodic oscillations has not received much attention. This study experimentally documents forced synchronization of the quasiperiodic state and the internally locked state of a thermoacoustic oscillator system. This system consists of a gas-filled resonance tube with a nonuniform cross-sectional area. The thermoacoustic oscillator was designed and built in such a way that nonlinear interactions between the fundamental acoustic oscillation mode and the third mode of the gas column are controlled by a temperature difference that is locally created in the resonance tube. Bifurcation diagrams were mapped out by changing the forcing strength and frequency. Separated Arnold tongues were found and both modes were entrained to the external force through complete synchronization. A saddle-node bifurcation was observed in the route from partial to complete synchronization when the forcing strength was relatively weak. However, a Hopf (torus-death) bifurcation was observed when the forcing was relatively strong. In the internally locked state, the bifurcation occurred after the internal locking was broken down by the external force.
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Affiliation(s)
- M Sato
- Department of Mechanical Systems Engineering, Tohoku University, Sendai 980-8579, Japan
| | - H Hyodo
- Department of Mechanical Systems Engineering, Tohoku University, Sendai 980-8579, Japan
| | - T Biwa
- Department of Mechanical Systems Engineering, Tohoku University, Sendai 980-8579, Japan
| | - R Delage
- Department of Management Science and Technology, Tohoku University, Sendai 980-8579, Japan
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Maguire OR, Wong ASY, Baltussen MG, van Duppen P, Pogodaev AA, Huck WTS. Dynamic Environments as a Tool to Preserve Desired Output in a Chemical Reaction Network. Chemistry 2020; 26:1676-1682. [PMID: 31808965 DOI: 10.1002/chem.201904725] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Revised: 11/28/2019] [Indexed: 12/31/2022]
Abstract
Current efforts to design functional molecular systems have overlooked the importance of coupling out-of-equilibrium behaviour with changes in the environment. Here, the authors use an oscillating reaction network and demonstrate that the application of environmental forcing, in the form of periodic changes in temperature and in the inflow of the concentration of one of the network components, removes the dependency of the periodicity of this network on temperature or flow rates and enforces a stable periodicity across a wide range of conditions. Coupling a system to a dynamic environment can thus be used as a simple tool to regulate the output of a network. In addition, the authors show that coupling can also induce an increase in behavioural complexity to include quasi-periodic oscillations.
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Affiliation(s)
- Oliver R Maguire
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525, AJ, Nijmegen, The Netherlands
| | - Albert S Y Wong
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA, 02138, USA
| | - Mathieu G Baltussen
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525, AJ, Nijmegen, The Netherlands
| | - Peer van Duppen
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525, AJ, Nijmegen, The Netherlands
| | - Aleksandr A Pogodaev
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525, AJ, Nijmegen, The Netherlands
| | - Wilhelm T S Huck
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525, AJ, Nijmegen, The Netherlands
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Voorsluijs V, Kevrekidis IG, De Decker Y. Nonlinear behavior and fluctuation-induced dynamics in the photosensitive Belousov-Zhabotinsky reaction. Phys Chem Chem Phys 2017; 19:22528-22537. [PMID: 28809962 DOI: 10.1039/c7cp03260a] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
The photosensitive Belousov-Zhabotinsky (pBZ) reaction has been used extensively to study the properties of chemical oscillators. In particular, recent experiments revealed the existence of complex spatiotemporal dynamics for systems consisting of coupled micelles (V < 10-21 L) or droplets (V ≈ [10-8-10-11] L) in which the pBZ reaction takes place. These results have been mostly understood in terms of reaction-diffusion models. However, in view of the small size of the droplets and micelles, large fluctuations of concentrations are to be expected. In this work, we investigate the role of fluctuations on the dynamics of a single droplet with stochastic simulations of an extension of the Field-Körös-Noyes (FKN) model taking into account the photosensitivity. The birhythmicity and chaotic behaviors predicted by the FKN model in the absence of fluctuations become transient or intermittent regimes whose lifetime decreases with the size of the droplet. Simple oscillations are more robust and can be observed even in small systems (V > 10-12 L), which justifies the use of deterministic models in microfluidic systems of coupled oscillators. The simulations also reveal that fluctuations strongly affect the efficiency of inhibition by light, which is often used to control the kinetics of these systems: oscillations are found for parameter values for which they are supposed to be quenched according to deterministic predictions.
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Affiliation(s)
- Valérie Voorsluijs
- Center for Nonlinear Phenomena and Complex Systems (CENOLI), Université libre de Bruxelles (ULB), Campus Plaine, C.P. 231, B-1050 Brussels, Belgium.
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6
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Čupić Ž, Marković VM, Maćešić S, Stanojević A, Damjanović S, Vukojević V, Kolar-Anić L. Dynamic transitions in a model of the hypothalamic-pituitary-adrenal axis. CHAOS (WOODBURY, N.Y.) 2016; 26:033111. [PMID: 27036189 DOI: 10.1063/1.4944040] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamic-pituitary-adrenal (HPA) axis were systematically investigated. Conditions under which qualitative transitions between dynamic states occur are determined by independently varying the rate constants of all reactions that constitute the model. Bifurcation types were further characterized using continuation algorithms and scale factor methods. Regions of bistability and transitions through supercritical Andronov-Hopf and saddle loop bifurcations were identified. Dynamic state analysis predicts that the HPA axis operates under basal (healthy) physiological conditions close to an Andronov-Hopf bifurcation. Dynamic properties of the stress-control axis have not been characterized experimentally, but modelling suggests that the proximity to a supercritical Andronov-Hopf bifurcation can give the HPA axis both, flexibility to respond to external stimuli and adjust to new conditions and stability, i.e., the capacity to return to the original dynamic state afterwards, which is essential for maintaining homeostasis. The analysis presented here reflects the properties of a low-dimensional model that succinctly describes neurochemical transformations underlying the HPA axis. However, the model accounts correctly for a number of experimentally observed properties of the stress-response axis. We therefore regard that the presented analysis is meaningful, showing how in silico investigations can be used to guide the experimentalists in understanding how the HPA axis activity changes under chronic disease and/or specific pharmacological manipulations.
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Affiliation(s)
- Željko Čupić
- Department of Catalysis and Chemical Engineering, Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
| | - Vladimir M Marković
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, 11158 Belgrade, Serbia
| | - Stevan Maćešić
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, 11158 Belgrade, Serbia
| | - Ana Stanojević
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, 11158 Belgrade, Serbia
| | - Svetozar Damjanović
- Institute of Endocrinology, Diabetes and Metabolic Diseases, School of Medicine, University of Belgrade, Dr Subotica 13, 11000 Belgrade, Serbia
| | - Vladana Vukojević
- Department of Clinical Neuroscience, Karolinska Institutet, CMM L8:01, 17176 Stockholm, Sweden
| | - Ljiljana Kolar-Anić
- Department of Catalysis and Chemical Engineering, Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
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Pejić N, Kolar-Anić L, Maksimović J, Janković M, Vukojević V, Anić S. Dynamic transitions in the Bray–Liebhafsky oscillating reaction. Effect of hydrogen peroxide and temperature on bifurcation. REACTION KINETICS MECHANISMS AND CATALYSIS 2016. [DOI: 10.1007/s11144-016-0984-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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8
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St-Yves G, Davidsen J. Defect mediated turbulence in a locally quasiperiodic chemical medium. J Chem Phys 2010; 133:044909. [DOI: 10.1063/1.3464493] [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
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9
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Silva LC, Faria RB. Complex dynamic behavior in the bromate-oxalic acid-acetone-Mn(II) oscillating reaction in a continuous stirred tank reactor (CSTR). Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.04.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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10
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Feedback Analysis of Mechanisms for Chemical Oscillators. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141281.ch3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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11
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Koper MT. Oscillations and Complex Dynamical Bifurcations in Electrochemical Systems. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141519.ch2] [Citation(s) in RCA: 95] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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12
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Schmitz G, Kolar-Anić L, Anić S, Grozdić T, Vukojević V. Complex and chaotic oscillations in a model for the catalytic hydrogen peroxide decomposition under open reactor conditions. J Phys Chem A 2006; 110:10361-8. [PMID: 16928130 DOI: 10.1021/jp063519b] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Numerous periodic and aperiodic dynamic states obtained in a model for hydrogen peroxide decomposition in the presence of iodate and hydrogen ions (the Bray-Liebhafsky reaction) realized in an open reactor (CSTR), where the flow rate was the control parameter, have been investigated numerically. Between two Hopf bifurcation points, different simple and complex oscillations and different routes to chaos were observed. In the region of the mixed-mode evolution of the system, the transitions between two successive mixed-mode simple states are realized by period-doubling of the initial state leading to a chaotic window in which the next dynamic state emerges mixed with the initial one. It appears in increasing proportions in concatenated patterns until total domination. Thus, with increasing flow rate the period-doubling route to chaos was obtained, whereas with decreasing flow rate the peak-adding route to chaos was obtained. Moreover, in very narrow regions of flow rates, chaotic mixtures of mixed-mode patterns were observed. This evolution of patterns repeats until the end of the mixed-mode region at high flow rates that corresponds to chaotic mixtures of one large and many small amplitude oscillations. Starting from the reverse Hopf bifurcation point and decreasing the flow rate, simple small amplitude sinusoidal oscillations were encountered and then the period-doubling route to chaos. With a further decreasing flow rate, the mixed-mode oscillations emerge inside the chaotic window.
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Affiliation(s)
- Guy Schmitz
- Faculté des Sciences Appliqués, Université Libre de Bruxelles, CP165/63, Av. Roosevelt 50, 1050 Bruxelles, Belgium
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13
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Park JS, Lee KJ. Line-defects-mediated complex-oscillatory spiral waves in a chemical system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066219. [PMID: 16906958 DOI: 10.1103/physreve.73.066219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2005] [Revised: 05/11/2006] [Indexed: 05/11/2023]
Abstract
In this paper, we summarize our experimental observations on complex-oscillatory spiral waves that arise in a Belousov-Zhabotinsky (BZ) reaction-diffusion system. The observed wave structures generically bear line defects across which the phase of local oscillation changes by a multiple of 2 pi. The local oscillation at every spatial point along a line defect of period-2 (P-2) oscillatory media is period-1 (P-1) oscillatory. For the homogeneous BZ reaction can be excitable, simply periodic, complex periodic, or chaotic as the control parameters are tuned, a number of different complex wave states are revealed. A two-dimensional phase diagram, which includes domains of P-2 oscillatory spirals, intermittently breathing spirals, period-3 (P-3) oscillatory spirals, two different types of mixed-mode periodic spirals, and line-defect-mediated turbulence, is constructed. Several different transitions among different dynamic states are described systematically. In all cases, line defects are found to play an important role.
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Affiliation(s)
- Jin-Sung Park
- National Creative Research Initiative Center for Neuro-dynamics and Department of Physics, Korea University, Seoul 136-701, Korea
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14
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Spears BK, Szeri AJ. A new route to chaos: sequences of topological torus bifurcations. CHAOS (WOODBURY, N.Y.) 2005; 15:33108. [PMID: 16252982 DOI: 10.1063/1.2005167] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
We consider a sequence of topological torus bifurcations (TTBs) in a nonlinear, quasiperiodic Mathieu equation. The sequence of TTBs and an ensuing transition to chaos are observed by computing the principal Lyapunov exponent over a range of the bifurcation parameter. We also consider the effect of the sequence on the power spectrum before and after the transition to chaos. We then describe the topology of the set of knotted tori that are present before the transition to chaos. Following the transition, solutions evolve on strange attractors that have the topology of fractal braids in Poincare sections. We examine the topology of fractal braids and the dynamics of solutions that evolve on them. We end with a brief discussion of the number of TTBs in the cascade that leads to chaos.
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Affiliation(s)
- Brian K Spears
- Department of Mechanical Engineering, University of California, Berkeley, California 94720-1740, USA
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15
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Kalishyn YY, Rachwalska M, Khavrus VO, Strizhak PE. The effect of oxygen on time-dependent bifurcations in the Belousov–Zhabotinsky oscillating chemical reaction in a batch. Phys Chem Chem Phys 2005; 7:1680-6. [DOI: 10.1039/b416006a] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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16
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Affiliation(s)
- Raima Larter
- Department of Chemistry, Indiana University−Purdue University at Indianapolis, 402 North Blackford Street, Indianapolis, Indiana 46202
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17
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Salmon JB, Colin A, Roux D. Dynamical behavior of a complex fluid near an out-of-equilibrium transition: approaching simple rheological chaos. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:031505. [PMID: 12366118 DOI: 10.1103/physreve.66.031505] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2002] [Indexed: 05/23/2023]
Abstract
We report here an extensive study of sustained oscillations of the viscosity of a complex fluid near an out-of-equilibrium transition. Using well defined protocols, we perform rheological measurements of the onion texture near a layering transition in a Couette flow. This complex fluid exhibits sustained oscillations of the viscosity, on a large time scale (500 s) at controlled stress. These oscillations are directly correlated to an oscillating microstructural change of the texture of the fluid. We observe a great diversity of dynamical behavior and show that there is a coupling with spatial effects in the inverted Delta v direction. This is in agreement with a careful analysis of the temporal series of the viscosity with the dynamical system theory. This analysis indicates that the observed dynamical responses do not strictly correspond to three-dimensional chaotic states, probably because some spatiotemporal effects are present and are likely to play an important role.
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Wunenburger AS, Colin A, Leng J, Arnéodo A, Roux D. Oscillating viscosity in a lyotropic lamellar phase under shear flow. PHYSICAL REVIEW LETTERS 2001; 86:1374-1377. [PMID: 11178087 DOI: 10.1103/physrevlett.86.1374] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2000] [Indexed: 05/23/2023]
Abstract
We report some time-dependent behavior of lyotropic lamellar phase under shear flow. At fixed stress, near a layering instability, the system presents an oscillating shear rate. We build up a new stress versus shear rate diagram that includes temporal behavior. This diagram is made of two distinct branches of stationary states which correspond, respectively, to disordered and ordered multilamellar vesicle phases. When increasing the shear stress, prior to the transition to the ordered structural state, sustained oscillations of the viscosity are recorded. They correspond to periodic structural change of the entire sample between a disordered and a ordered state of multilamellar vesicles.
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Affiliation(s)
- A S Wunenburger
- Centre de Recherche Paul Pascal, CNRS, Av. Dr. A. Schweitzer, 33600 Pessac, France
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19
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Li YN, Song H, Cai ZS, Chen L, Hou Z, Wei QL, Wu BX, Zhao XZ. New chaotic behavior and its effective control in BelousovZhabotinsky reaction. CAN J CHEM 2001. [DOI: 10.1139/v00-166] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
A new "spiral-in-to-spiral-out" mixed-mode type chaos of the BelousovZhabotinsky (BZ) reaction in a continuous flow stirred tank reactor (CSTR) is observed. We discussed its evolution and characterization in detail. We controlled the new chaos into steady periodic behavior by two control methods: (i) a self-adaptive delayed feedback controlling scheme; and (ii) a linear self-interacting feedback controlling scheme.Key words: BZ-CSTR reaction, chaos, control.
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Kawczyński AL, Strizhak PE. Period adding and broken Farey tree sequence of bifurcations for mixed-mode oscillations and chaos in the simplest three-variable nonlinear system. J Chem Phys 2000. [DOI: 10.1063/1.481222] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Griffith TM, Edwards DH. Integration of non-linear cellular mechanisms regulating microvascular perfusion. Proc Inst Mech Eng H 1999; 213:369-83. [PMID: 10581964 DOI: 10.1243/0954411991534988] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
It is becoming increasingly evident that interactions between the different cell types present in the vessel wall and the physical forces that result from blood flow are highly complex. This short article will review evidence that irregular fluctuations in vascular resistance are generated by non-linearity in the control mechanisms intrinsic to the smooth muscle cell and can be classified as chaotic. Non-linear systems theory has provided insights into the mechanisms involved at the cellular level by allowing the identification of dominant control variables and the construction of one-dimensional iterative maps to model vascular dynamics. Experiments with novel peptide inhibitors of gap junctions have shown that the coordination of aggregate responses depends on direct intercellular communication. The sensitivity of chaotic trajectories to perturbation may nevertheless generate a high degree of variability in the response to pharmacological interventions and altered perfusion conditions.
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Affiliation(s)
- T M Griffith
- Department of Diagnostic Radiology, University of Wales College of Medicine, Cardiff, UK
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De Brouwer S, Edwards DH, Griffith TM. Simplification of the quasiperiodic route to chaos in agonist-induced vasomotion by iterative circle maps. THE AMERICAN JOURNAL OF PHYSIOLOGY 1998; 274:H1315-26. [PMID: 9575937 DOI: 10.1152/ajpheart.1998.274.4.h1315] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
We have shown that the patterns of vasomotion induced by histamine in isolated rabbit ear resistance arteries can be described in terms of iterative circle maps that model the dynamics of coupled nonlinear oscillators. Cyclopiazonic acid (CPA), an inhibitor of the sarcoplasmic reticulum Ca(2+)-adenosinetriphosphatase pump, consistently transformed chaotic behavior into characteristic periodic oscillations known as mixed-mode responses, which consist of mixtures of large- and small-amplitude excursions and represent frequency-locked states. Quasiperiodicity, which reflects the interaction of oscillators with incommensurate frequencies, was also observed, although in a smaller number of experiments. The patterns of mixed-mode complexes found at different CPA concentrations allowed the derivation of firing numbers, i.e., number of large oscillations/sum of number of small and large oscillations, and the sequences in which they emerged conformed to Farey arithmetic. Two-dimensional return maps derived by Poincaré section of phase space representations of the dynamics were used to compute the mean number of rotations per iteration on the circle, i.e., the winding number. Plots of winding number against firing number revealed a devil's staircase-type structure. Experiments with verapamil, a voltage-operated L-type Ca(2+)-channel antagonist, confirmed that influx of extracellular Ca2+ was essential to sustain chaos, quasiperiodicity, and mixed-mode responses. Nonlinear coupling between cytosolic and membrane events in rabbit ear arteries thus results in a self-organized dynamics that collapses to that predicted by the theory of simple circle maps.
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Affiliation(s)
- S De Brouwer
- Department of Diagnostic Radiology, University of Wales College of Medicine, Heath Park, Cardiff, United Kingdom
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Strizhak PE, Didenko OZ. Analysis of the effect of temperature on complex self-oscillation regimes in the belousov-zhabotinskii reaction in a constant-agitation flow-through reactor. THEOR EXP CHEM+ 1997. [DOI: 10.1007/bf02765910] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Noskov OV, Karavaev AD, Kazakov VP, Spivak SI. Quasiperiodic to bursting oscillations transition in the model of the Belousov–Zhabotinsky reaction. MENDELEEV COMMUNICATIONS 1997. [DOI: 10.1070/mc1997v007n01abeh000649] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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25
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Bronnikova TV, Schaffer WM, Olsen LF. Quasiperiodicity in a detailed model of the peroxidase–oxidase reaction. J Chem Phys 1996. [DOI: 10.1063/1.472927] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Vekilov PG, Alexander JI, Rosenberger F. Nonlinear response of layer growth dynamics in the mixed kinetics-bulk-transport regime. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:6650-6660. [PMID: 9965891 DOI: 10.1103/physreve.54.6650] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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27
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Strizhak PE, Pojman JA. Infinite period and Hopf bifurcations for the pH-regulated oscillations in a semibatch reactor (H(2)O(2)-Cu(2+)-S(2)O(2-) (3)-NaOH system). CHAOS (WOODBURY, N.Y.) 1996; 6:461-465. [PMID: 12780276 DOI: 10.1063/1.166188] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Dynamic behavior of the pH-regulated oscillations has been studied for the hydrogen peroxide oxidation of thiosulfate ions in the presence of trace amounts of copper(II) ions in a semibatch reactor. A solution of 0.08 M Na(2)S(2)O(3) and 0.112 M NaOH was flowed at 0.160 mL/min into 300 mL of solution containing the H(2)O(2) and Cu(2+) in a vessel. There exists a critical value of the H(2)O(2) or Cu(2+) concentrations below which the system does not oscillate. The oscillations appear due to an infinite period bifurcation at low initial concentrations of the H(2)O(2). The initial concentration of Cu(2+) may be considered as a bifurcation parameter in this case. Increase of the initial hydrogen peroxide concentration causes the pH-regulated oscillations through a nondegenerate supercritical Hopf bifurcation. The classification of bifurcations is based on the analysis of the behavior of oscillation amplitude and period at different initial concentrations of the H(2)O(2) and Cu(2+). Our results show a possibility to distinguish different scenarios for the appearance of transient oscillations in semibatch experiments. (c) 1996 American Institute of Physics.
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Affiliation(s)
- Peter E. Strizhak
- L. V. Pisarzhevskii Institute of Physical Chemistry, National Academy of Sciences of Ukraine, Prospect Nauki 31, Kiev 252028, UkraineDepartment of Chemistry and Biochemistry, University of Southern Mississippi, Hattiesburg, Mississippi 39406-5043
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28
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Stirring-induced bifurcation driven by the chaotic regime in the Belousov—Zhabotinsky reaction in a CSTR. Chem Phys Lett 1995. [DOI: 10.1016/0009-2614(95)00883-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Wang J, Sørensen PG, Hynne F. Transient Complex Oscillations in the Closed Belousov-Zhabotinsky Reaction: Experimental and Computational Studies. Z PHYS CHEM 1995. [DOI: 10.1524/zpch.1995.192.part_1.063] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Strizhak PE, Didenko OZ. Effect of temperature on bifurcation of self-oscillating modes in the Belousov-Zhabotinskii reaction in a continuous-flow stirred-tank reactor. THEOR EXP CHEM+ 1995. [DOI: 10.1007/bf00529986] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Effects of Macromixing on the oregonator model of the belousov — zhabotinsky reaction in a stirred reactor. Chem Eng Sci 1994. [DOI: 10.1016/0009-2509(94)00278-9] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Strizhak PE. Classical and quantum properties of a simple autocatalytic mechanism ? The Lotka-Volterra system. THEOR EXP CHEM+ 1994. [DOI: 10.1007/bf00520259] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Zhang D, Gyorgyi L, Peltier WR. Deterministic chaos in the Belousov-Zhabotinsky reaction: Experiments and simulations. CHAOS (WOODBURY, N.Y.) 1993; 3:723-745. [PMID: 12780076 DOI: 10.1063/1.165933] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
An account of the experimental discovery of complex dynamical behavior in the continuous-flow, stirred tank reactor (CSTR) Belousov-Zhabotinsky (BZ) reaction, as well as numerical simulations based on the BZ chemistry are given. The most recent four- and three-variable models that are deduced from the well-accepted, updated chemical mechanism of the BZ reaction and which exhibit robust chaotic states are summarized. Chaos has been observed in experiments and simulations embedded in the regions of complexities at both low and high flow rates. The deterministic nature of the observed aperiodicities at low flow rates is unequivocally established. However, controversy still remains in the interpretation of certain aperiodicities observed at high flow rates.
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Affiliation(s)
- Dongmei Zhang
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, CanadaInstitute of Inorganic and Analytical Chemistry, Lorand Eotvos University, Budapest H-1528, HungaryDepartment of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
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Ibison P, Scott SK. Detailed bifurcation structure and new mixed-mode oscillations of the Belousov–Zhabotinskii reaction in a stirred flow reactor. ACTA ACUST UNITED AC 1990. [DOI: 10.1039/ft9908603695] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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