Transition from spiral wave chimeras to phase cluster states

Totz, Jan Frederik; Tinsley, Mark R.; Engel, Harald; Showalter, Kenneth

doi:10.1038/s41598-020-64081-6

Cited by 17 publications

(4 citation statements)

References 40 publications

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“…Recently, it has shown that chimera states may also exit in the human brain under some conditions such as epileptic seizures [43]. Chimera states are not only observed in one dimensional systems [1] but also in two or three dimensional systems [40,41,[46][47][48][49][50][51][52][53][54][55][56][57][58][59]. One of the most remarkable examples in the two dimensional system is the so-called spiral wave chimera which combines the features of spiral waves and chimera states [39][40][41][46][47][48][49][50][51][52][53][54][55][56][57].…”

Section: Introductionmentioning

confidence: 99%

“…Chimera states are not only observed in one dimensional systems [1] but also in two or three dimensional systems [40,41,[46][47][48][49][50][51][52][53][54][55][56][57][58][59]. One of the most remarkable examples in the two dimensional system is the so-called spiral wave chimera which combines the features of spiral waves and chimera states [39][40][41][46][47][48][49][50][51][52][53][54][55][56][57]. Differing from the classic spiral wave whose core center is a phase singularity (or topological defect) at which the amplitude drops to zero, the core region of the spiral wave chimera consists of a group of desynchronized oscillators running at full amplitude [39][40][41].…”

Section: Introductionmentioning

confidence: 99%

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Spiral wave chimera states in populations of oscillators mediated by a slowly varying diffusive environment

Yang¹,

He²,

2021

Preprint

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Chimera states are usually observed in oscillator systems with nonlocal couplings. Such a nonlocal coupling arises typically as oscillators are coupled via an external environment which changes so fast that it could be eliminated adiabatically. Here we for the first time report the existence of spiral wave chimera states in large populations of Stuart-Landau oscillators coupled via a slowly changing diffusive environment under which the adiabatic approximation breaks down. The transition from spiral wave chimeras to spiral waves with the smooth core and to unstable spiral wave chimeras as functions of the system parameters are exploited. The phenomenological mechanism for explaining the formation of spiral wave chimeras is also proposed. The existence of spiral wave chimeras and the underlying mechanism are further confirmed in a three-component FitzHugh-Nagumo system with the similar environmental coupling scheme. Our results provide important hints to seek chimera patterns in both laboratory and realistic chemical or biological systems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spiral wave chimera states in populations of oscillators mediated by a slowly varying diffusive environment

Yang¹,

He²,

2021

Preprint

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“…Later, the appearance of such exotic chimera patterns was verified theoretically in a handful [70][71][72][73][74][75] of RD and non-RD systems. Apart from these studies, there exist some experimental evidences [76][77][78] which reveal the emergence of spiral chimera states in coupled Belousov-Zhabotinsky chemical oscillators.…”

Section: Introductionmentioning

confidence: 99%

Amplitude mediated spiral chimera pattern in a nonlinear reaction-diffusion system

Kundu,

Muruganandam,

Ghosh

et al. 2021

Preprint

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Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study which is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state having spatial coexistence of coherent and incoherent dynamics in a system of identically interacting individuals. In the present article, we report the emergence of various collective dynamical patterns while considering a system of prey-predator dynamics in presence of a two-dimensional diffusive environment. Particularly, we explore the observance of four distinct categories of spatial arrangements among the species, namely spiral wave, spiral chimera, completely synchronized oscillations, and oscillation death states in a broad region of the diffusion-driven parameter space. Emergence of amplitude mediated spiral chimera states displaying drifted amplitudes and phases in the incoherent subpopulation is detected for parameter values beyond both Turing and Hopf bifurcations. Transition scenarios among all these distinguishable patterns are numerically demonstrated for a wide range of the diffusion coefficients which reveal that the chimera states arise during the transition from oscillatory to steady state dynamics. Furthermore, we characterize the occurrence of each of the recognizable patterns by estimating the strength of incoherent subpopulations in the two-dimensional space.

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“…Interestingly, it is shown that despite of the incoherent inner core, spiral wave is propagating stably in the outer region. Discovered by Shima and Kuramoto in 2004 in nonlocally coupled periodic oscillators [39], SWC has received growing interest in the field of nonlinear science in recent years, particularly for researchers working on pattern formations in reaction-diffusion (RD) systems [53][54][55][56][57][58][59][60][61][62][63][64][65][66]. For the model of nonlocally coupled phase oscillators, an analytical description of SWC has been given in Ref.…”

Section: Introductionmentioning

confidence: 99%

Spiral wave chimeras in reaction-diffusion systems: phenomenon, mechanism and transitions

Li,

He,

et al. 2020

Preprint

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Spiral wave chimeras (SWCs), which combine the features of spiral waves and chimera states, are a new type of dynamical patterns emerged in spatiotemporal systems due to the spontaneous symmetry breaking of the system dynamics. In generating SWC, the conventional wisdom is that the dynamical elements should be coupled in a nonlocal fashion. For this reason, it is commonly believed that SWC is excluded from the general reaction-diffusion (RD) systems possessing only local couplings. Here, by an experimentally feasible model of three-component FitzHugh-Nagumo-type RD system, we demonstrate that, even though the system elements are locally coupled, stable SWCs can still be observed in a wide region in the parameter space. The properties of SWCs are explored, and the underlying mechanisms are analyzed from the point view of coupled oscillators. Transitions from SWC to incoherent states are also investigated, and it is found that SWCs are typically destabilized in two scenarios, namely core breakup and core expansion. The former is characterized by a continuous breakup of the single asynchronous core into a number of small asynchronous cores, whereas the latter is featured by the continuous expansion of the single asynchronous core to the whole space. Remarkably, in the scenario of core expansion, the system may develop into an intriguing state in which regular spiral waves are embedded in a completely disordered background. This state, which is named shadowed spirals, manifests from a new perspective the coexistence of incoherent and coherent states in spatiotemporal systems, generalizing therefore the traditional concept of chimera states. Our studies provide an affirmative answer to the observation of SWCs in RD systems, and pave a way to the realization of SWCs in experiments.

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Transition from spiral wave chimeras to phase cluster states

Cited by 17 publications

References 40 publications

Spiral wave chimera states in populations of oscillators mediated by a slowly varying diffusive environment

Spiral wave chimera states in populations of oscillators mediated by a slowly varying diffusive environment

Amplitude mediated spiral chimera pattern in a nonlinear reaction-diffusion system

Spiral wave chimeras in reaction-diffusion systems: phenomenon, mechanism and transitions

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