Globally clustered chimera states in delay-coupled populations

Sheeba, Jane H.; Chandrasekar, V. K.; Lakshmanan, M.

doi:10.1103/physreve.79.055203

Cited by 78 publications

(54 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) and discovered a motivating phenomenon of the existence of GCC states (note that system (1) consists of two populations of identical oscillators) as shown in Fig. 1, and reported briefly in [13]. Interestingly enough we found that the coupling delay induces such phenomena where the system of identical delay-coupled populations splits into desynchronized and synchronized groups.…”

Section: Numerical Studiesmentioning

confidence: 67%

“…These boundaries are the same as those for the in-phase and anti-phase synchronization states obtained from Eq. (13). Dot-dashed and dashed curves correspond to in-phase and anti-phase synchronization states of (16).…”

Section: Applicationsmentioning

confidence: 99%

“…In this paper, following our Rapid Communication [13], we present a more detailed discussion of the effects of coupling delay in inducing chimera and globally clustered chimera (GCC) states in systems of coupled identical oscillator populations. By a GCC state, here we mean a state where the system splits into two different groups, one synchronized and the other desynchronized, each group comprised of oscillators from both the populations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chimera and globally clustered chimera: Impact of time delay

2010

Self Cite

View full text Add to dashboard Cite

Following a short report of our preliminary results [Phys. Rev. E 79, 055203(R) (2009)], we present a more detailed study of the effects of coupling delay in diffusively coupled phase oscillator populations. We find that coupling delay induces chimera and globally clustered chimera (GCC) states in delay coupled populations. We show the existence of multi-clustered states that act as link between the chimera and the GCC states. A stable GCC state goes through a variety of GCC states, namely periodic, aperiodic, long-and short-period breathers and becomes unstable GCC leading to global synchronization in the system, on increasing time delay. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.

show abstract

Section: Numerical Studiesmentioning

confidence: 67%

Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chimera and globally clustered chimera: Impact of time delay

2010

Self Cite

View full text Add to dashboard Cite

show abstract

“…One proven modification is the inclusion of non-local effects of the geometry of the system that has been shown to lead to a co-existence of partially synchronized and partially asynchronized states of oscillators as a steady-state solution. Such states, addressed as chimera states, are the subject of recent theoretical and experimental studies (Kuramoto and Battogtokh, 2002;Abrams and Strogatz, 2004;Abrams et al, 2008;Ko and Ermentrout, 2008;Omel'chenko et al, 2008;Sethia et al, 2008;Sheeba et al, 2009;Laing, 2009a, b;Laing et al, 2012;Martens et al, 2013;Yao et al, 2013;Rothkegel and Lehnertz, 2014;Kapitaniak et al, 2014;Pazó and Montbrió, 2014;Panaggio and Abrams, 2014;Zhu et al, 2014;Gupta et al, 2014;Vasudevan and Cavers, 2014a, b). We focus our present study on defining a Kuramoto model with a phase lag that would accommodate the existence of chimera states.…”

Section: Mathematical Model Of the Earthquake Sequencingmentioning

confidence: 99%

Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs

Vasudevan

Cavers

Ware

2015

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

Abstract. Earthquake sequencing studies allow us to investigate empirical relationships among spatio-temporal parameters describing the complexity of earthquake properties. We have recently studied the relevance of Markov chain models to draw information from global earthquake catalogues. In these studies, we considered directed graphs as graph theoretic representations of the Markov chain model and analyzed their properties. Here, we look at earthquake sequencing itself as a directed graph. In general, earthquakes are occurrences resulting from significant stress interactions among faults. As a result, stress-field fluctuations evolve continuously. We propose that they are akin to the dynamics of the collective behavior of weakly coupled non-linear oscillators. Since mapping of global stress-field fluctuations in real time at all scales is an impossible task, we consider an earthquake zone as a proxy for a collection of weakly coupled oscillators, the dynamics of which would be appropriate for the ubiquitous Kuramoto model. In the present work, we apply the Kuramoto model with phase lag to the nonlinear dynamics on a directed graph of a sequence of earthquakes. For directed graphs with certain properties, the Kuramoto model yields synchronization, and inclusion of nonlocal effects evokes the occurrence of chimera states or the co-existence of synchronous and asynchronous behavior of oscillators. In this paper, we show how we build the directed graphs derived from global seismicity data. Then, we present conditions under which chimera states could occur and, subsequently, point out the role of the Kuramoto model in understanding the evolution of synchronous and asynchronous regions. We surmise that one implication of the emergence of chimera states will lead to investigation of the present and other mathematical models in detail to generate global chimera-state maps similar to global seismicity maps for earthquake forecasting studies.

show abstract

“…It was shown that in a globally coupled network of oscillators with delay feedback, the single spatially connected region was replaced by a number of spatially disconnected regions of coherence with regions of incoherence in between. These states were named clustered chimera states [9,10]. Chimera states have been described as the natural link between coherent and incoherent states [11].…”

Section: Introductionmentioning

confidence: 99%

Chimera states in coupled sine-circle map lattices

Nayak¹,

Gupte²

2011

AIP Conference Proceedings

View full text Add to dashboard Cite

Systems of coupled oscillators have been seen to exhibit chimera states, i.e. states where the system splits into two groups where one group is phase locked and the other is phase randomized. In this work, we report the existence of chimera states in a system of two interacting populations of sine circle maps. This system also exhibits the clustered chimera behavior seen earlier in delay coupled systems. Rich spatio-temporal behavior is seen in different regimes of the phase diagram. We carry out a detailed analysis of the stability regimes and map out the phase diagram using numerical and analytic techniques.

show abstract

Globally clustered chimera states in delay-coupled populations

Cited by 78 publications

References 30 publications

Chimera and globally clustered chimera: Impact of time delay

Chimera and globally clustered chimera: Impact of time delay

Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs

Chimera states in coupled sine-circle map lattices

Contact Info

Product

Resources

About