Chimera states are chaotic transients

Wolfrum, Matthias; Omel’chenko, Oleh

doi:10.1103/physreve.84.015201

Cited by 268 publications

(339 citation statements)

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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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confidence: 99%

Chimera Death: Symmetry Breaking in Dynamical Networks

2014

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“…Classical chimera states have a dynamical character, however they have a long life duration. They correspond then to a metastable regime (until the collapses studied in [5] for finite size chains) and not to a short life transient regime. Moreover for some classical models of infinite chains [1], the classical chimera states present an infinite life duration and correspond to a permanent regime.…”

Section: Quantum Chimera Statesmentioning

confidence: 96%

“…This behaviour is in accordance with the Poisson distribution of the LSD which is not characteristic to a quantum chaotic behaviour but to a quantum pseudorandom behaviour. In comparison with the classical case, if the model (1) presents chimera states which are always transient chaotic as shown in [5], the main characteristic of the classical chimera states are the coexistence of ordered and disordered dynamics in the same chain. The disordered dynamics is not necessary chaotic.…”

Section: Chaotic Behaviourmentioning

confidence: 99%

“…The particularity of such states is a part of the oscillator set exhibits an ordered dynamics (synchronized oscillations) whereas another part exhibits a disordered dynamics (desynchronized oscillations without correlation between the oscillators). This regime is not transient during a short time, these intriguing states have got a long and sometimes an infinite life duration: disorder does not spread to the whole set and the disordered part does not collapse to synchronized oscillations in a short time (see [5] to find a discussion concerning the life duration of chimera states). These states have been called chimera, in reference to the mythological creature hybrid of a lion, a snake and a goat.…”

Section: Introductionmentioning

confidence: 99%

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Quantum chimera states

Viennot

Aubourg

2016

Physics Letters A

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We study a theoretical model of closed quasi-hermitian chain of spins which exhibits quantum analogues of chimera states, i.e. long life classical states for which a part of an oscillator chain presents an ordered dynamics whereas another part presents a disordered dynamics. For the quantum analogue, the chimera behavior deals with the entanglement between the spins of the chain. We discuss the entanglement properties, quantum chaos, quantum disorder and semiclassical similarity of our quantum chimera system. The quantum chimera concept is novel and induces new perspectives concerning the entanglement of multipartite systems.

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“…However, the stability of chimera states in finitely discretized systems is questioned. In fact, it is reported that when N is finite, chimera states with the sine coupling are chaotic transient and finally collapse into the completely synchronous solution [12,13,26]. Recently, Ashwin and Burylko proposed the weak chimera similar to the chimera state, which is defined by the coexistence of frequency-synchronous and -asynchronous oscillators in the systems of coupled indistinguishable phase oscillators but is not necessarily spatially structured as coherent and incoherent domains [28].…”

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Persistent chimera states in nonlocally coupled phase oscillators

Suda

Okuda

2015

Phys. Rev. E

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Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this Rapid Communication, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that chimera states can be stable even without taking the continuous limit, which we call the persistent chimera state. The behavior of coupled oscillator systems can describe various pattern formations in a wide range of scientific fields [1,2]. In the systems of nonlocally coupled identical oscillators, there often appears a strange phenomenon called the chimera state, which is characterized by the coexistence of coherent and incoherent domains, where the former domain consists of phase-locked oscillators and the latter domain consists of drifting oscillators with spatially changing frequencies . This interesting phenomenon was first discovered in the system of nonlocally coupled phase oscillators obeying the evolution equationwith 2π -periodic phases θ (x) on a finite interval x ∈ [0,1] under the periodic boundary condition, a smooth 2π -periodic coupling function , and the kernel G(y) = (κ/2) exp(−κ|y|), where a constant 1/κ denotes the coupling range [3]. Recently, similar spatiotemporal patterns have been found in various systems using, e.g., the logistic maps [14,15], Rössler systems [15], and FitzHugh-Nagumo oscillators [18].In the study of the chimera state, the system, Eq. (1), with the sine coupling [27]is particularly important because of its simplicity and generality. In fact, this coupling function was used also in the first discovery of the chimera state [3]. For numerical simulations, we usually discretize Eq. (1) into such form as Eq. (3). In the simulations of such discretized systems, we can confirm that chimera states are surely stable in the continuous limit N → ∞. However, the stability of chimera states in finitely discretized systems is questioned. In fact, it is reported that when N is finite, chimera states with the sine coupling are chaotic transient and finally collapse into the completely synchronous solution [12,13,26]. Recently, Ashwin and Burylko proposed the weak chimera similar to the chimera state, which is defined by the coexistence of frequency-synchronous and -asynchronous oscillators in the systems of coupled indistinguishable phase oscillators but is not necessarily spatially structured as coherent and incoherent domains [28]. They studied the weak chimera in some types of networks composed of the minimal number of oscillators with the Hansel-Mato-Meunier coupling, Eq. (4), and demonstrated that the weak chimera can be persistent (nontransient). In this Rapid Communication, we study chimera states in the systems of nonlocally coupled phase oscillators with the Hansel-MatoMeunier coupling b...

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Chimera states are chaotic transients

Cited by 268 publications

References 35 publications

Chimera Death: Symmetry Breaking in Dynamical Networks

Chimera Death: Symmetry Breaking in Dynamical Networks

Quantum chimera states

Persistent chimera states in nonlocally coupled phase oscillators

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