Heteroclinic switching between chimeras

Bick, Christian

doi:10.1103/physreve.97.050201

Cited by 48 publications

(45 citation statements)

References 46 publications

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“…Moreover, as we show below, the switching observed here is critical-the transition rate depends on noise intensity as a power law and switching can be triggered by arbitrarily small noise. This power-law dependence distinguishes switching chimeras from previously reported "alternating chimeras," in which either the transitions are forced by large fluctuation terms [20,[56][57][58] or rely on heteroclinic dynamics [62][63][64]. In the first case, there are finite barriers separating the different states, while in the second case each state is inherently unstable and switching occurs in the absence of noise.…”

Section: Computational Observation Of Switching Chimerasmentioning

confidence: 63%

“…Despite previous progress [98], the underlying mechanism of lateral switching remains elusive. This is especially the case for aperiodic lateral switching, since such cases cannot be easily modeled by hypothesizing the existence of a central pattern generator or propagating wave dynamics, as in previous alternating chimeras [56,62,63]. In the case of the songbird zebra finches, for instance, the inter-hemispheric switching between song-control areas of the brain is highly irregular, characterized by switching intervals ranging from 4 ms to 150 ms [93].…”

Section: Connections With Biological and Other Physical Systemsmentioning

confidence: 99%

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Critical Switching in Globally Attractive Chimeras

et al. 2020

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We report on a new type of chimera state that attracts almost all initial conditions and exhibits power-law switching behavior in networks of coupled oscillators. Such switching chimeras consist of two symmetric configurations, which we refer to as subchimeras, in which one cluster is synchronized and the other is incoherent. Despite each subchimera being linearly stable, switching chimeras are extremely sensitive to noise: arbitrarily small noise triggers and sustains persistent switching between the two symmetric subchimeras. The average switching frequency increases as a power law with the noise intensity, which is in contrast with the exponential scaling observed in typical stochastic transitions. Rigorous numerical analysis reveals that the power-law switching behavior originates from intermingled basins of attraction associated with the two subchimeras, which in turn are induced by chaos and symmetry in the system. The theoretical results are supported by experiments on coupled optoelectronic oscillators, which demonstrate the generality and robustness of switching chimeras. arXiv:1911.07871v1 [cond-mat.dis-nn]

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Section: Computational Observation Of Switching Chimerasmentioning

confidence: 63%

Section: Connections With Biological and Other Physical Systemsmentioning

confidence: 99%

Critical Switching in Globally Attractive Chimeras

et al. 2020

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“…Multi-body interactions are an unavoidable consequence of phase reduction, but save for a few works [12,16,58,61,62], the role of multi-body phase interactions shaping exotic dynamics remains largely unexplored. In the weak-coupling regime of the MF-CGLE, multi-body phase interactions are essential to describe all states apart from FS and UIS.…”

Section: E Conclusionmentioning

confidence: 99%

Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation

León

Pazó

2019

Phys. Rev. E

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Phase reduction is a powerful technique that makes possible to describe the dynamics of a weakly perturbed limit-cycle oscillator in terms of its phase. For ensembles of oscillators, a classical example of phase reduction is the derivation of the Kuramoto model from the mean-field complex Ginzburg-Landau equation (MF-CGLE). Still, the Kuramoto model is a first-order phase approximation that displays either full synchronization or incoherence, but none of the nontrivial dynamics of the MF-CGLE. This fact calls for an expansion beyond the first order in the coupling constant. We develop an isochron-based scheme to obtain the second-order phase approximation, which reproduces the weak coupling dynamics of the MF-CGLE. The practicality of our method is evidenced by extending the calculation up to third order. Each new term of the power series expansion contributes with additional higher-order multi-body (i.e. non-pairwise) interactions. This points to intricate multi-body phase interactions as the source of pure collective chaos in the MF-CGLE at moderate coupling. II. MEAN-FIELD COMPLEX GINZBURG-LANDAU EQUATIONThe MF-CGLE consists of N diffusively coupled Stuart-Landau oscillators governed by N coupled (complex-valued)

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“…These interactions include higher harmonics; in particular, for r > 0 the calculations above imply that both SSS and DDD are linearly stable. Moreover, for α := α 2 = α 4 − π 2 we obtain the same parametrization as in [18,19]. (13), on broken lines by (16), and on solid lines by (17).…”

Section: Heteroclinic Cycles For Two Oscillators Per Populationmentioning

confidence: 84%

“…This work is organized as follows. In this paper, we build on results in a recent brief communication [18] to prove the existence of robust heteroclinic cycles between localized frequency synchrony; in a companion paper [19] we give a detailed discussion of the stability of such heteroclinic cycles (which may be embedded into larger heteroclinic structures). The remainder of this paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Heteroclinic Dynamics of Localized Frequency Synchrony: Heteroclinic Cycles for Small Populations

Bick

2019

J Nonlinear Sci

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Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay of network structure and interaction. Here, we give results for small networks on the existence of heteroclinic cycles between dynamically invariant sets on which the oscillators show localized frequency synchrony. Trajectories near these heteroclinic cycles will exhibit sequential switching of localized frequency synchrony: a population oscillators in the network will oscillate faster (or slower) than others and which population has this property changes sequentially over time. Since we give explicit conditions on the system parameters for such dynamics to arise, our results give insights into how network structure and interactions (which include higher-order interactions between oscillators) facilitate heteroclinic switching between localized frequency synchrony.

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Heteroclinic switching between chimeras

Cited by 48 publications

References 46 publications

Critical Switching in Globally Attractive Chimeras

Critical Switching in Globally Attractive Chimeras

Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation

Heteroclinic Dynamics of Localized Frequency Synchrony: Heteroclinic Cycles for Small Populations

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