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Chaubey N, Kumar Shaw P, Mukherjee S, Sen A. Phase switching phenomenon in a system of three coupled DC glow discharge plasmas. Chaos 2023; 33:033125. [PMID: 37003831 DOI: 10.1063/5.0130226] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Accepted: 02/27/2023] [Indexed: 06/19/2023]
Abstract
We report the first experimental observations of phase switching in a system of three coupled plasma sources. Two of the plasma sources are inductively coupled to each other while the third one is directly coupled to one of them. The coupled system acquires a frequency pulling synchronized state following which a transition occurs to a frequency entrainment state with an increase in the frequency of the directly coupled system. We also observe a sudden jump from a lower to a higher frequency entrainment state and a concomitant phase switching between the oscillations of the two directly coupled sources while the phase difference between the inductively coupled sources remains constant. These experimental findings are established using various diagnostic tools, such as the Fourier spectra, frequency bifurcation plots, Lissajous plots, and Hilbert transforms of the data. The experimental results are qualitatively modeled using three coupled van der Pol equations, in which two of them are environmentally coupled while the third one is directly coupled with one of them.
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Affiliation(s)
- Neeraj Chaubey
- Institute for Plasma Research, Gandhinagar 382428, India
| | - Pankaj Kumar Shaw
- Raja Peary Mohan College, University of Calcutta, Uttarpara, West Bengal, India
| | - S Mukherjee
- Institute for Plasma Research, Gandhinagar 382428, India
| | - A Sen
- Institute for Plasma Research, Gandhinagar 382428, India
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2
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Roy T, Chaurasia SS, Parmananda P. Phase-flip transition in volume-mismatched pairs of coupled 1-pentanol drops. Phys Rev E 2022; 106:034614. [PMID: 36266858 DOI: 10.1103/physreve.106.034614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Accepted: 09/07/2022] [Indexed: 06/16/2023]
Abstract
We have explored a variety of synchronization domains and observed phase-flip transition in a pair of coupled 1-pentanol drops as a function of the volume mismatch. Both experimental observations and numerical studies are presented. The experiments were carried out in a rectangular channel in a ferroin deionized water solution premixed with some volume of pentanol. A single pentanol drop (≥ 3μL) performs back and forth oscillations along the length of the channel due to the well-known Marangoni forces. In the present work, for a pair of drops, the drop 1 volume was changed from 3 to 5 μL in steps of 1μL, whereas the drop 2 volume was varied from 1 to 3 μL in steps of 0.5μL. A systematic investigation of all the possible combinations of the drop volumes showed the presence of three different types of synchrony-in-phase, antiphase, and phase-switched. In-phase synchronization was robust for a volume mismatch of >3.0μL between the two drops. On the other hand, antiphase synchronization was robust when the volume mismatch was <2.0μL. The phase-switched state is a synchronized state involving a phase-flip transition in the time domain. This state was observed for the intermediate range of volume mismatch. Numerically, the system has been investigated using two Stuart-Landau oscillators interacting via a coupling function in the form of Lennard-Jones potential. The numerical results suitably capture both in-phase and antiphase oscillations for a pair of volume-mismatched pentanol drops.
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Affiliation(s)
- Tanushree Roy
- Department of Physics, IIT Bombay, Mumbai-400076, Maharashtra, India
| | | | - P Parmananda
- Department of Physics, IIT Bombay, Mumbai-400076, Maharashtra, India
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Korkmaz N. A Phase Control Method for the Dynamical Attractor of the HR Neuron Model: The Rotation-Transition Process and Its Experimental Realization. Neural Process Lett 2021; 53:3877-3892. [DOI: 10.1007/s11063-021-10568-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Aravind M, Sinha S, Parmananda P. Competitive interplay of repulsive coupling and cross-correlated noises in bistable systems. Chaos 2021; 31:061106. [PMID: 34241287 DOI: 10.1063/5.0056173] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 05/25/2021] [Indexed: 06/13/2023]
Abstract
The influence of noise on synchronization has potential impact on physical, chemical, biological, and engineered systems. Research on systems subject to common noise has demonstrated that noise can aid synchronization, as common noise imparts correlations on the sub-systems. In our work, we revisit this idea for a system of bistable dynamical systems, under repulsive coupling, driven by noises with varying degrees of cross correlation. This class of coupling has not been fully explored, and we show that it offers new counter-intuitive emergent behavior. Specifically, we demonstrate that the competitive interplay of noise and coupling gives rise to phenomena ranging from the usual synchronized state to the uncommon anti-synchronized state where the coupled bistable systems are pushed to different wells. Interestingly, this progression from anti-synchronization to synchronization goes through a domain where the system randomly hops between the synchronized and anti-synchronized states. The underlying basis for this striking behavior is that correlated noise preferentially enhances coherence, while the interactions provide an opposing drive to push the states apart. Our results also shed light on the robustness of synchronization obtained in the idealized scenario of perfectly correlated noise, as well as the influence of noise correlation on anti-synchronization. Last, the experimental implementation of our model using bistable electronic circuits, where we were able to sweep a large range of noise strengths and noise correlations in the laboratory realization of this noise-driven coupled system, firmly indicates the robustness and generality of our observations.
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Affiliation(s)
- Manaoj Aravind
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Sudeshna Sinha
- Indian Institute of Science Education and Research Mohali, Knowledge City, SAS Nagar, Sector 81, Manauli, Punjab P.O. 140306, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
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Sharma J, Tiwari I, Das D, Parmananda P. Chimeralike states in a minimal network of active camphor ribbons. Phys Rev E 2021; 103:012214. [PMID: 33601538 DOI: 10.1103/physreve.103.012214] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 01/04/2021] [Indexed: 06/12/2023]
Abstract
A chimeralike state is the spatiotemporal pattern in an ensemble of homogeneous coupled oscillators, described as the emergence of coexisting coherent (synchronized) and incoherent (unsynchronized) groups. We demonstrate the existence of these states in three active camphor ribbons, which are camphor infused rectangular pieces of paper. These pinned ribbons rotate on the surface of the water due to Marangoni effect driven forces generated by the surface tension gradients. The ribbons are coupled via a camphor layer on the surface of the water. In the minimal network of globally coupled camphor ribbons, chimeralike states are characterized by the coexistence of two synchronized and one unsynchronized ribbons. We present a numerical model, simulating the coupling between ribbons as repulsive Yukawa interactions, which was able to reproduce these experimentally observed states.
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Affiliation(s)
- Jyoti Sharma
- Department of Physics, Indian Institute of Technology - Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Ishant Tiwari
- Department of Physics, Indian Institute of Technology - Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Dibyendu Das
- Department of Physics, Indian Institute of Technology - Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology - Bombay, Powai, Mumbai, Maharashtra 400076, India
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Yao C, He Z, Zou W. Oscillation behavior driven by processing delay in diffusively coupled inactive systems: Cluster synchronization and multistability. Chaos 2020; 30:123137. [PMID: 33380058 DOI: 10.1063/5.0025958] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
Couplings involving time delay play a relevant role in the dynamical behavior of complex systems. In this work, we address the effect of processing delay, which is a specific kind of coupling delay, on the steady state of general nonlinear systems and prove that it may drive the system to Hopf bifurcation and, in turn, to a rich oscillatory behavior. Additionally, one may observe multistable states and size-dependent cluster synchronization. We derive the analytic conditions to obtain an oscillatory regime and confirm the result by numerically simulated experiments on different oscillator networks. Our results demonstrate the importance of processing delay for complex systems and pave the way for a better understanding of dynamical control and synchronization in oscillatory networks.
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Affiliation(s)
- Chenggui Yao
- College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314000, China
| | - Zhiwei He
- Department of Mathematics, Shaoxing University, Shaoxing 312000, China
| | - Wei Zou
- School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
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Sharma J, Tiwari I, Das D, Parmananda P, Pimienta V. Rotational synchronization of camphor ribbons in different geometries. Phys Rev E 2020; 101:052202. [PMID: 32575261 DOI: 10.1103/physreve.101.052202] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Accepted: 04/05/2020] [Indexed: 06/11/2023]
Abstract
We present experiments on multiple pinned self-propelled camphor ribbons, which is a rectangular piece of paper with camphor infused in its matrix. Experiments were performed on three, four, and five ribbons placed in linear and polygonal geometries. The pinned ribbons rotate on the surface of water, due to the surface tension gradient introduced by the camphor layer in the neighborhood of the ribbon. This camphor layer leads to a chemical coupling between the ribbons. In different geometries, the ribbons have been observed to rotationally synchronize in all the possible configurations. A numerical model, emulating the interactions between the ribbons as Yukawa interaction was studied, which was qualitatively able to reproduce the experimental findings.
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Affiliation(s)
- Jyoti Sharma
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Ishant Tiwari
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Dibyendu Das
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Véronique Pimienta
- Laboratoire des IMRCP, Université de Toulouse, CNRS UMR 5623, Université Paul Sabatier, Toulouse Cedex 9, France
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Abstract
Experiments on interacting pinned self-propelled rotators are presented. The rotators are made from paper with camphor infused in its matrix. The ribbons rotate due to Marangoni effect driven forces arising by virtue of surface tension gradients. Two such self-rotating camphor ribbons are observed to experience a repulsive coupling via the camphor layer in the common water medium. Lag synchronization in both corotating (same sense of rotation) and counterrotating (opposite sense of rotation) ribbons is reported for the experiments. This synchronization is found to be dependent on the pivot to pivot distance l. For distances less than the span of both the ribbons, l_{c}, the rotators successfully synchronize. Furthermore, it is experimentally perceived that synchronization in the counterrotating ribbons is more robust than in the corotating ribbons. We rationalize the mechanism of this synchronization via a theoretical model involving a Yukawa type interaction which is analyzed numerically.
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Affiliation(s)
- Jyoti Sharma
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
| | - Ishant Tiwari
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
| | - Dibyendu Das
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
| | - V S Akella
- Department of Applied Mechanics, Indian Institute of Technology, Madras, Adyar, Chennai, Tamil Nadu 600036, India
| | - Véronique Pimienta
- Laboratoire des IMRCP, Université de Toulouse, CNRS UMR 5623, Université Paul Sabatier, 118 route de Narbonne 31062, Toulouse Cedex 9, France
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Manoj K, Pawar SA, Sujith RI. Experimental Evidence of Amplitude Death and Phase-Flip Bifurcation between In-Phase and Anti-Phase Synchronization. Sci Rep 2018; 8:11626. [PMID: 30072725 DOI: 10.1038/s41598-018-30026-3] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Accepted: 07/18/2018] [Indexed: 11/30/2022] Open
Abstract
Nonlinear phenomena emerging from the coupled behaviour of a pair of oscillators have attracted considerable research attention over the years, of which, amplitude death (AD) and phase-flip bifurcation (PFB) are two noteworthy examples. Although theoretical research has postulated the coexistence of AD and PFB upon variation of different control parameters, such an occurrence has not been reported in practical systems. Here, we provide the first experimental evidence of the coexistence of AD and PFB in a physical system, comprising of a coupled pair of candle-flame oscillators. As the strength of coupling between the oscillators is increased, we report a decrease in the span of AD region between the states of in-phase and anti-phase oscillations, leading up to a point of PFB. Understanding such a switching of phenomena between AD and PFB helps us to evade their undesirable occurrences such as AD in neuron and brain cells, oscillatory state in prey-predator systems, oscillatory spread of epidemics and so forth.
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Hankins MJ, Wickramasinghe M, Kiss IZ. Synchronization of current oscillations in a dual-anode dissolution reaction in the presence of a common cathode electrode. Electrochim Acta 2017; 252:76-83. [DOI: 10.1016/j.electacta.2017.08.153] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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11
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Chaubey N, Mukherjee S, Sen A, Iyengar ANS. Experimental observation of phase-flip transitions in two inductively coupled glow discharge plasmas. Phys Rev E 2017; 94:061201. [PMID: 28085372 DOI: 10.1103/physreve.94.061201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2016] [Indexed: 11/07/2022]
Abstract
We report an experimental observation of a phase-flip transition in the frequency synchronization of two dc glow discharge plasma sources that are coupled in a noninvasive fashion. When the fundamental oscillation frequency of the potential fluctuations of one of the sources is progressively increased, by raising its discharge voltage, a frequency pulling regime is observed, followed by a synchronized regime that shows a frequency jump phenomenon. The jump is associated with a phase-flip transition that takes the synchronized state from an in-phase to an antiphase state. When the process is reversed, the transition takes place at a different frequency, thereby exhibiting a hysteresis effect. A heuristic model, consisting of two van der Pol oscillators that are coupled to each other through a dynamic common medium, eminently captures the essential features of our experimental observations.
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Affiliation(s)
- Neeraj Chaubey
- Institute for Plasma Research, HBNI, Bhat, Gandhinagar 382428, India
| | - S Mukherjee
- Institute for Plasma Research, HBNI, Bhat, Gandhinagar 382428, India
| | - A Sen
- Institute for Plasma Research, HBNI, Bhat, Gandhinagar 382428, India
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12
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Sharma A, Verma UK, Shrimali MD. Phase-flip and oscillation-quenching-state transitions through environmental diffusive coupling. Phys Rev E 2016; 94:062218. [PMID: 28085412 DOI: 10.1103/physreve.94.062218] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2016] [Indexed: 11/07/2022]
Abstract
We study the dynamics of nonlinear oscillators coupled through environmental diffusive coupling. The interaction between the dynamical systems is maintained through its agents which, in turn, interact globally with each other in the common dynamical environment. We show that this form of coupling scheme can induce an important transition like phase-flip transition as well transitions among oscillation quenching states in identical limit-cycle oscillators. This behavior is analyzed in the parameter plane by analytical and numerical studies of specific cases of the Stuart-Landau oscillator and van der Pol oscillator. Experimental evidences of the phase-flip transition and quenching states are shown using an electronic version of the van der Pol oscillators.
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Affiliation(s)
- Amit Sharma
- The Institute of Mathematical Science, CIT Campus, Taramani, Chennai 600113, India
| | - Umesh Kumar Verma
- Department of Physics, Central University of Rajasthan, Ajmer 305 817, India
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, Ajmer 305 817, India
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Abstract
The phase-flip transition has been demonstrated in a host of coupled nonlinear oscillator models, many pertaining directly to understanding neural dynamics. However, there is little evidence that this phenomenon occurs in the brain. Using simultaneous microelectrode recordings in the nonhuman primate cerebral cortex, we demonstrate the presence of phase-flip transitions between oscillatory narrow-band local field potential signals separated by several centimeters. Specifically, we show that sharp transitions between in-phase and antiphase synchronization are accompanied by a jump in synchronization frequency. These findings are significant for two reasons. First, they validate predictions made by model systems. Second, they have potentially far reaching implications for our understanding of the mechanisms underlying corticocortical communication, which are thought to rely on narrow-band oscillatory synchronization with specific relative phase relationships.
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Affiliation(s)
- Nicholas M Dotson
- Cell Biology and Neuroscience, Montana State University, Bozeman, Montana 59717, USA
| | - Charles M Gray
- Cell Biology and Neuroscience, Montana State University, Bozeman, Montana 59717, USA
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Chandrasekar VK, Gopal R, Senthilkumar DV, Lakshmanan M. Phase-flip chimera induced by environmental nonlocal coupling. Phys Rev E 2016; 94:012208. [PMID: 27575124 DOI: 10.1103/physreve.94.012208] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2016] [Indexed: 06/06/2023]
Abstract
We report the emergence of a collective dynamical state, namely, the phase-flip chimera, from an ensemble of identical nonlinear oscillators that are coupled indirectly via the dynamical variables from a common environment, which in turn are nonlocally coupled. The phase-flip chimera is characterized by the coexistence of two adjacent out-of-phase synchronized coherent domains interspersed by an incoherent domain, in which the nearby oscillators are in out-of-phase synchronized states. Attractors of the coherent domains are either from the same or from different basins of attractions, depending on whether they are periodic or chaotic. The conventional chimera precedes the phase-flip chimera in general. Further, the phase-flip chimera emerges after the completely synchronized evolution of the ensemble, in contrast to conventional chimeras, which emerge as an intermediate state between completely incoherent and coherent states. We have also characterized the observed dynamical transitions using the strength of incoherence, probability distribution of the correlation coefficient, and framework of the master stability function.
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Affiliation(s)
- V K Chandrasekar
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA University, Thanjavur 613 401, India
| | - R Gopal
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
- Department of Physics, Nehru Memorial College, Puthanampatti, Tiruchirapalli 621 007, India
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695 016, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
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Proskurkin IS, Vanag VK. Dynamical regimes of two frequency different chemical oscillators coupled via pulse inhibitory coupling with time delay. Russ J Phys Chem 2014. [DOI: 10.1134/s0036024415020223] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Punetha N, Prasad A, Ramaswamy R. Phase-locked regimes in delay-coupled oscillator networks. Chaos 2014; 24:043111. [PMID: 25554031 DOI: 10.1063/1.4897360] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
For an ensemble of globally coupled oscillators with time-delayed interactions, an explicit relation for the frequency of synchronized dynamics corresponding to different phase behaviors is obtained. One class of solutions corresponds to globally synchronized in-phase oscillations. The other class of solutions have mixed phases, and these can be either randomly distributed or can be a splay state, namely with phases distributed uniformly on a circle. In the strong coupling limit and for larger networks, the in-phase synchronized configuration alone remains. Upon variation of the coupling strength or the size of the system, the frequency can change discontinuously, when there is a transition from one class of solutions to another. This can be from the in-phase state to a mixed-phase state, but can also occur between two in-phase configurations of different frequency. Analytical and numerical results are presented for coupled Landau-Stuart oscillators, while numerical results are shown for Rössler and FitzHugh-Nagumo systems.
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Affiliation(s)
- Nirmal Punetha
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Awadhesh Prasad
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
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Affiliation(s)
- Anastasia I Lavrova
- Immanuel Kant Baltic Federal University, A.Nevskogo str. 14A, Kaliningrad, 236041, Russia.
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Abstract
Time delayed coupling plays a crucial role in determining the system's dynamics. We here report that the time delay induces transition from the asynchronous state to the complete synchronization (CS) state in the repulsively coupled chaotic oscillators. In particular, by changing the coupling strength or time delay, various types of synchronous patterns, including CS, antiphase CS, antiphase synchronization (ANS), and phase synchronization, can be generated. In the transition regions between different synchronous patterns, bistable synchronous oscillators can be observed. Furthermore, we show that the time-delay-induced phase flip bifurcation is of key importance for the emergence of CS. All these findings may light on our understanding of neuronal synchronization and information processing in the brain.
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Affiliation(s)
- Chenggui Yao
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, People's Republic of China
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Saxena G, Prasad A, Ramaswamy R. Amplitude death phenomena in delay-coupled Hamiltonian systems. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 87:052912. [PMID: 23767603 DOI: 10.1103/physreve.87.052912] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2012] [Revised: 04/12/2013] [Indexed: 06/02/2023]
Abstract
Hamiltonian systems, when coupled via time-delayed interactions, do not remain conservative. In the uncoupled system, the motion can typically be periodic, quasiperiodic, or chaotic. This changes drastically when delay coupling is introduced since now attractors can be created in the phase space. In particular, for sufficiently strong coupling there can be amplitude death (AD), namely, the stabilization of point attractors and the cessation of oscillatory motion. The approach to the state of AD or oscillation death is also accompanied by a phase flip in the transient dynamics. A discussion and analysis of the phenomenology is made through an application to the specific cases of harmonic as well as anharmonic coupled oscillators, in particular the Hénon-Heiles system.
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Affiliation(s)
- Garima Saxena
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
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Abstract
We study the dynamics of nonlinear oscillators indirectly coupled through a dynamical environment or a common medium. We observed that this form of indirect coupling leads to synchronization and phase-flip transition in periodic as well as chaotic regime of oscillators. The phase-flip transition from in- to anti-phase synchronization or vise-versa is analyzed in the parameter plane with examples of Landau-Stuart and Rössler oscillators. The dynamical transitions are characterized using various indices such as average phase difference, frequency, and Lyapunov exponents. Experimental evidence of the phase-flip transition is shown using an electronic version of the van der Pol oscillators.
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Affiliation(s)
- Amit Sharma
- The LNM Institute of Information Technology, Jaipur 302031, India
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