Publisher's Note: Chimera and globally clustered chimera: Impact of time delay [Phys. Rev. E<b>81</b>, 046203 (2010)]

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

doi:10.1103/physreve.81.049906

Cited by 30 publications

(40 citation statements)

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“…In recent times several theoretical studies [16][17][18][19][20] and experimental investigations [21][22][23][24][25] have established chimera as a robust concept occurring in varied complex networks, including chaotic dynamical systems [21,26,27]. For example networks of chaotic dynamical systems with nonlocal coupling exhibit coexisting spatial domains of coherence and incoherence [26,27], coherent travelling waves [28] and spiral wave chimera states [29].…”

Section: Introductionmentioning

confidence: 99%

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

Gopal

Chandrasekar

Venkatesan³

et al. 2014

Phys. Rev. E

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By developing the concepts of strength of incoherence and discontinuity measure, we show that a distinct quantitative characterization of chimera and multichimera states which occur in networks of coupled nonlinear dynamical systems admitting nonlocal interactions of finite radius can be made. These measures also clearly distinguish between chimera/multichimera states (both stable and breathing types) and coherent and incoherent as well as cluster states. The measures provide a straight forward and precise characterization of the various dynamical states in coupled chaotic dynamical systems irrespective of the complexity of the underlying attractors.

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Section: Introductionmentioning

confidence: 99%

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

Gopal

Chandrasekar

Venkatesan³

et al. 2014

Phys. Rev. E

Self Cite

174

160

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“…They have been the subject of intensive theoretical investigations, e.g. [4][5][6][7][8][9][10][11][12][13][14][15]. Experimental evidence of chimeras has only recently been provided for optical [16], chemical [17], mechanical [18] and electronic [19] systems.…”

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confidence: 99%

Chimera Death: Symmetry Breaking in Dynamical Networks

2014

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For a network of generic oscillators with nonlocal topology and symmetry-breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent and incoherent domains) and oscillation death (oscillation suppression), which we call chimera death. We show that due to the interplay of nonlocality and breaking of rotational symmetry by the coupling two distinct scenarios from oscillatory behavior to a stationary state regime are possible: a transition from an amplitude chimera to chimera death via in-phase synchronized oscillations, and a direct abrupt transition for larger coupling strength. Spontaneous symmetry breaking in a complex dynamical system is a fundamental and universal phenomenon which occurs in diverse fields such as physics, chemistry, and biology [1]. It implies that processes occurring in nature favor a less symmetric configuration, although the underlying principles can be symmetric. This intriguing concept has recently gained renewed interest generated by the enormous burst of works on chimera states and on oscillation death, which have emerged independently. In this Letter we draw a relation between these two.Chimera states correspond to the situation when an ensemble of identical elements self-organizes into two coexisting and spatially separated domains with dramatically different behavior, i.e., spatially coherent and incoherent oscillations [2,3]. They have been the subject of intensive theoretical investigations, e.g. [4][5][6][7][8][9][10][11][12][13][14][15]. Experimental evidence of chimeras has only recently been provided for optical [16], chemical [17], mechanical [18] and electronic [19] systems. These peculiar hybrid states may also account for the observation of partial synchrony in neural activity [20], like unihemispheric sleep, i.e., the ability of some birds or dolphins to sleep with one half of their brain while the other half remains aware [21,22]. Chimera states have been initially found for phase oscillators [2], and they typically occur in networks with nonlocal coupling. Recently, for globally coupled oscillators it has been shown that such spatio-temporal patterns can be also connected to the amplitude dynamics (amplitude-mediated chimeras) [23,24]. However, the global coupling topology does not provide a clear notion of space, which is crucial for chimera states. A further open question is whether chimeras can be extended to more general symmetry breaking states.Another fascinating effect which requires the break-up of the system's symmetry as a crucial ingredient is oscillation death which refers to stable inhomogeneous steady states (IHSS) which are created through the coupling of self-sustained oscillators. This regime occurs when a ho- * corresponding author: schoell@physik.tu-berlin.de mogeneous steady state splits into at least two distinct branches -upper and lower -which represent a newly created IHSS [25][26][27][28]. For a network of coupled elements oscillation death ...

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“…Besides, chimera states are thought to occur near the stability boundaries of order and disordered states in systems with delayed coupling [47,48]. Here we observe in-phase chimera states near the bistability region of in-phase and anti-phase states.…”

Section: Discussionmentioning

confidence: 53%

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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Publisher's Note: Chimera and globally clustered chimera: Impact of time delay [Phys. Rev. E81, 046203 (2010)]

Cited by 30 publications

References 0 publications

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

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

Chimera Death: Symmetry Breaking in Dynamical Networks

Mobility-induced persistent chimera states

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