Spiral wave chimera states in large populations of coupled chemical oscillators

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

doi:10.1038/s41567-017-0005-8

Cited by 201 publications

(141 citation statements)

References 27 publications

(23 reference statements)

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“…The investigation of emergent behaviors in coupled populations of oscillators continues to be an active area of research [2], [4], [36], [30]. PRCs and associated phase models (3) provide first order approximations to phase dynamics resulting from small perturbations; reduction technique allows for complicated models to be analyzed in a more tractible coordinate system.…”

Section: Higher Order Approximations Of Coupling Functionsmentioning

confidence: 99%

Recent advances in coupled oscillator theory

Ermentrout

Park

Wilson

2019

Phil. Trans. R. Soc. A.

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We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems with applications to the Izhikevich neuron. We then introduce the idea of isostable reduction to explore behaviors that the weak coupling paradigm cannot explain. In an additional example, we show how bifurcations that change the stability of phase locked solutions in a pair of identical coupled neurons can be understood using the notion of isostable reduction.

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Section: Higher Order Approximations Of Coupling Functionsmentioning

confidence: 99%

Recent advances in coupled oscillator theory

Ermentrout

Park

Wilson

2019

Phil. Trans. R. Soc. A.

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“…In addition to the phase coupled oscillator systems mentioned above, this kind of spatiotemporal behaviour has also been seen to exist in other oscillator systems. These include non-locally coupled complex Ginzburg-Landau oscillators 1 , delay-coupled rings of phase oscillators 6 , bipartite oscillator populations 7,8 , Stuart-Landau oscillators 9 , networks of Kuramoto oscillators 10,11 , coupled chemical oscillators [12][13][14] , and mechanical oscillator networks 15 . The detailed analysis of oscillator systems with different kinds of coupling has been reviewed recently by Omel'chenko 16 . arXiv:1907.04215v1 [nlin.CD] 6 Jul 2019…”

Section: Introductionmentioning

confidence: 99%

Chimera states in globally coupled sine circle map lattices: Spatiotemporal intermittency and hyperchaos

Singha

Gupte

2020

Physics Letters A

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We study the existence of chimera states, i.e. mixed states, in a globally coupled sine circle map lattice, with different strengths of inter-group and intra-group coupling. We find that at specific values of the parameters of the CML, a completely random initial condition evolves to chimera states, having a phase synchronised and a phase desynchronised group, where the space time variation of the phases of the maps in the desynchronised group shows structures similar to spatiotemporally intermittent regions. Using the complex order parameter we obtain a phase diagram that identifies the region in the parameter space which supports chimera states of this type, as well as other types of phase configurations such as globally phase synchronised states, two phase clustered states and fully phase desynchronised states. We estimate the volume of the basin of attraction of each kind of solution. The STI chimera region is studied in further detail via numerical and analytic stability analysis, and the Lyapunov spectrum is calculated. This state is identified to be hyperchaotic as the two largest Lyapunov exponents are found to be positive. The distributions of laminar and burst lengths in the incoherent region of the chimera show exponential behaviour. The average fraction of laminar/burst sites is identified to be the important quantity which governs the dynamics of the chimera. After an initial transient, these settle to steady values which can be used to reproduce the phase diagram in the chimera regime.The study of chimera states, i.e. mixed states where synchronised and desynchronised dynamics coexist, has been at the forefront of studies in nonlinear dynamics involving both theoretical and experimental systems. A variety of classes of chimera states, i.e. states which contain coexisting domains of distinct kinds of spatiotemporal behaviour can be seen. These include multi-headed chimera states, travelling chimera states, amplitude chimera states, twisted chimera states etc, and have been seen in coupled oscillator models such as the Kuramoto model,coupled Ginzburg-Landau oscillators and other systems. Here, we investigate chimera and other states in a coupled sine circle map lattice which is a discrete version of coupled oscillator systems. The CML consists of two populations of globally coupled identical sine circle maps with distinct values for the intergroup and intragroup coupling. We observe spatiotemporally intermittent chimeras, i.e. states which consist of a synchronised subgroup, and a state where coherent (phase synchronised) and incoherent (phase incoherent) domains co-exist, at low values of the nonlinearity map parameter. Such STI chimeras have been observed earlier in coupled oscillators models such as Stuart-Landau oscillators, Ginzburg-Landau oscillators, coupled optical resonators, chemical reactions etc. We analyse the STI chimera seen in the CML system by plotting the phase diagram of the system using the global order parameter, and identifying the region where STI chimeras can be seen. The basin...

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“…To provide insights into these processes and the use of BZ media for the applications above, previous studies utilised the BZ reaction in spatially confining media such as thin hydrogel films [41], small droplets in microfluidic devices [32,[42][43][44][45][46][47][48][49][50][51][52], vesicles [53][54][55][56][57], emulsions [58], BZ-AOT emulsions [9-11, 17, 59-64], cation exchange resins [65][66][67][68][69][70][71] and 3D printed structures [42,72,73].…”

Section: Introductionmentioning

confidence: 99%

Belousov–Zhabotinsky reaction in liquid marbles

et al. 2019

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In Belousov-Zhabotinsky (BZ) type reactions, chemical oxidation waves can be exploited to produce reaction-diffusion processors. This paper reports on a new method of encapsulating BZ solution in a powder coating of either polyethylene (PE) or polytetrafluoroethylene (PTFE), to produce BZ liquid marbles (LMs). BZ LMs have solid-liquid interfaces compared to previously reported encapsulation systems, BZ emulsions and BZ vesicles. Oscillation studies on individual LMs established PE-coated LMs were easier to prepare and more robust than PTFE-coated LMs. Therefore, this coating was used to study BZ LMs positioned in ordered and disordered arrays. Sporadic transfer of excitation waves was observed between LMs in close proximity to each other. These results lay the foundations for future studies on information transmission and processing arrays of BZ LMs. Future work aims to elucidate the effect of other physical stimuli on the dynamics of chemical excitation waves within these systems.

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Spiral wave chimera states in large populations of coupled chemical oscillators

Cited by 201 publications

References 27 publications

Recent advances in coupled oscillator theory

Recent advances in coupled oscillator theory

Chimera states in globally coupled sine circle map lattices: Spatiotemporal intermittency and hyperchaos

Belousov–Zhabotinsky reaction in liquid marbles

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