Transition from Amplitude to Oscillation Death via Turing Bifurcation

Koseska, Aneta; Volkov, E.I.; Kurths, Jürgen

doi:10.1103/physrevlett.111.024103

Cited by 166 publications

(163 citation statements)

References 45 publications

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“…(1) breaks the S 1 symmetry, which is a crucial condition to observe nontrivial inhomogeneous steady states z j = 0, i.e., oscillation death [28,29]. In the following we set the bifurcation parameter λ=1 and the oscillation frequency ω=2.…”

mentioning

confidence: 99%

Stability of amplitude chimeras in oscillator networks

Tumash¹,

Zakharova²,

Lehnert³

et al. 2017

EPL

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-We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase space structure. The existence of at least one positive real part of the Floquet exponents indicates an unstable manifold in phase space, which explains the nature of these states as long-living transients. Additionally, we find a Stuart-Landau network of minimum size N = 12 exhibiting amplitude chimeras.Introduction. -The dynamical state of networks of homogeneously coupled identical elements can show a peculiar behavior by self-organizing into two spatially separated domains with dramatically different behavior, e.g. a spatially coherent and a spatially incoherent region. This phenomenon was named chimera state by Abrams and Strogatz [1] after the Greek fire-breathing monster, whose body consists of different animals. These hybrid states were discovered for phase oscillators in the early 2000's by Kuramoto and Battogtokh [2]. They observed a spontaneous breakup of the system into spatially coexisting synchronized and desynchronized domains with respect to the phase.Chimera states have possible applications to neural activity [3,4], heart fibrillation [5] and social systems [6]. Chimera states were also associated with such phenomena as epileptic seizure [7] and unihemispheric sleep, which has been detected for some sea mammals and birds [8]. These creatures can sleep with only one half of their brain while the other half remains awake. For instance, this enables sleeping dolphins to detect predators and migrant birds can travel for hundreds of kilometers without having a break [9]. Recently, unihemispheric sleep has been found also for humans [10].Chimera states were initially found for coupled phase oscillators, where coherence is related to phase-and frequency-locked oscillators and incoherence is associated with drifting oscillators. Since then numerous chimera

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mentioning

confidence: 99%

Stability of amplitude chimeras in oscillator networks

Tumash¹,

Zakharova²,

Lehnert³

et al. 2017

EPL

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show abstract

“…The NIC is not necessary, if the buffer resistance is small. In addition, a recently found phenomenon of oscillation quenching in the systems of coupled nonlinear oscillators is worth mentioning [55][56][57][58]. It can manifest via two different mechanisms, the so-called oscillation death and amplitude death.…”

Section: Discussionmentioning

confidence: 99%

Stabilization of a Network of the FitzHugh–Nagumo Oscillators by Means of a Single Capacitor Based RC Filter Feedback Technique

et al. 2017

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We suggest employing the first-order stable RC filters, based on a single capacitor, for control of unstable fixed points in an array of oscillators. A single capacitor is sufficient to stabilize an entire array, if the oscillators are coupled strongly enough. An array, composed of 24 to 30 mean-field coupled FitzHugh-Nagumo (FHN) type asymmetric oscillators, is considered as a case study. The investigation has been performed using analytical, numerical, and experimental methods. The analytical study is based on the mean-field approach, characteristic equation for finding the eigenvalue spectrum, and the Routh-Hurwitz stability criteria using low-rank Hurwitz matrix to calculate the threshold value of the coupling coefficient. Experiments have been performed with a hardware electronic analog, imitating dynamical behavior of an array of the FHN oscillators.

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“…The simultaneous occurrence of AD and OD and the transition from AD to OD under diffusive coupling in coupled Stuart-Landau oscillators had been reported by Koseska et al in [12]. After then several works have been reported showing such transition in different coupled system like; mean field diffusive (MFD) coupled system [14], [15], time-delayed system [16], dynamic coupled system [17], conjugate coupled system [18], [19], diffusive and repulsive coupled system [20], [21] etc.…”

Section: Introductionmentioning

confidence: 94%

“…in laser [9], neuronal systems [10], [11], etc. In spite of this, it has found applications in diverse field [7], [12], [13].…”

Section: Introductionmentioning

confidence: 99%

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2018

IJET

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Transition from Amplitude to Oscillation Death via Turing Bifurcation

Cited by 166 publications

References 45 publications

Stability of amplitude chimeras in oscillator networks

Stability of amplitude chimeras in oscillator networks

Stabilization of a Network of the FitzHugh–Nagumo Oscillators by Means of a Single Capacitor Based RC Filter Feedback Technique

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