Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling

Gopal, R.; Chandrasekar, V. K.; Venkatesan, A.; Lakshmanan, M.

doi:10.1103/physreve.89.052914

Cited by 164 publications

(162 citation statements)

References 46 publications

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“…To calculate the mean phase velocity, the time interval is taken over 4 × 10 5 time units after an initial transient of 1 × 10 5 units. To clearly distinguish the disordered, chimera, multichimera and coherent states, we also use the recently introduced statistical measures by Gopal et al [27] using the time series of the network. For this purpose we will calculate the strength of incoherence (SI) and discontinuity measure (DM) from a local standard deviation analysis.…”

Section: Non-local Interactionmentioning

confidence: 99%

“…Consequently, the values of SI=1 or SI=0 or 0 < SI < 1 represent disordered, coherent and chimera or multi-chimera states respectively. Again in order to distinguish chimera and multi-chimera states we also introduce the so called discontinuity measure (DM) [27] which is defined as…”

Section: Non-local Interactionmentioning

confidence: 99%

“…In the case of global and local (nearest neighbor) coupling, the behavior of the stability function in incoherent, chimera and multi-chimera states are also discussed. In our analysis we have used suitable statistical measures recently introduced by Gopal et al [27] as well as the notion of mean phase velocity proposed by Omelchenko et al [28] to confirm the chimera and multi-chimera states.…”

Section: Introductionmentioning

confidence: 99%

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Chimera states in bursting neurons

2016

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We study the existence of chimera states in pulse-coupled networks of bursting Hindmarsh-Rose neurons with nonlocal, global and local (nearest neighbor) couplings. Through a linear stability analysis, we discuss the behavior of stability function in the incoherent (i.e. disorder), coherent, chimera and multi-chimera states. Surprisingly, we find that chimera and multi-chimera states occur even using local nearest neighbor interaction in a network of identical bursting neurons alone. This is in contrast with the existence of chimera states in populations of nonlocally or globally coupled oscillators. A chemical synaptic coupling function is used which plays a key role in the emergence of chimera states in bursting neurons. Existence of chimera, multi-chimera, coherent and disordered states are confirmed by means of the recently introduced statistical measures and mean phase velocity.

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Section: Non-local Interactionmentioning

confidence: 99%

Section: Non-local Interactionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chimera states in bursting neurons

2016

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“…There is not a unique method for discriminating chimeras which is useful for the vast variety of systems where they occur [54][55][56]. In the system considered here, a diversity of dynamical states are present together with chimera states, Fig.…”

Section: Appendix B: Classification Of Dynamical Statesmentioning

confidence: 99%

Mobility-induced persistent chimera states

2017

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We study the dynamics of mobile, locally coupled identical oscillators in the presence of coupling delays. We find different kinds of chimera states, in which coherent in-phase and anti-phase domains coexist with incoherent domains. These chimera states are dynamic and can persist for long times for intermediate mobility values. We discuss the mechanisms leading to the formation of these chimera states in different mobility regimes. This finding could be relevant for natural and technological systems composed of mobile communicating agents.

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“…Θ is the Heavyside step function, which selects only the groups which have a sufficiently large phase coherence so that the dispersion σ k is smaller than the prescribed threshold δ. Finally, we define the strength of incoherence S as [124,125] …”

Section: Phase Diagrams For Quenched and Annealed Disorder A Tramentioning

confidence: 99%

Dynamical phase transitions in generalized Kuramoto model with distributed Sakaguchi phase

Banerjee

2017

J. Stat. Mech.

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In this numerical work we have systematically studied the dynamical phase transitions in the KuramotoSakaguchi model of synchronizing phase oscillators controlled by disorder in the Sakaguchi phases. We find out the numerical steady state phase diagrams for quenched and annealed kinds of disorder in the Sakaguchi parameters using the conventional order parameter and other statistical quantities like strength of incoherence and discontinuity measures. We have also considered the correlation profile of the local order parameter fluctuations in the various identified phases. The phase diagrams for quenched disorder is qualitatively much different than those the global coupling regime. The order of various transitions are confirmed by a study of the distribution of the order parameter and its fourth order Binder's cumulant across the transition for an ensemble of initial distribution of phases. For annealed type of disorder, in contrast to the case with the quenched disorder, the system is almost insensitive to the amount of disorder. We also elucidate the role of chimeralike states in the synchronizing transition of the system and study the effect of disorder on these states. Finally, we seek justification of our results from simulations guided by the Ott-Antonsen ansatz.

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Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling

Cited by 164 publications

References 46 publications

Chimera states in bursting neurons

Chimera states in bursting neurons

Mobility-induced persistent chimera states

Dynamical phase transitions in generalized Kuramoto model with distributed Sakaguchi phase

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