Chimeras confined by fractal boundaries in the complex plane

Andrzejak, Ralph G.

doi:10.1063/5.0049631

Cited by 5 publications

(2 citation statements)

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“…Authors in 61 found highly riddled basins in small and highly symmetric all-to-all networks of coupled phase oscillators. Fractal basins of chimeras states were found in small networks of coupled complex maps 62 . In 54 the authors use a low-dimensional description valid for the infinite size system 63 to characterize the basin structure of different patterns in a model of two populations of all-to-all coupled Kuramoto oscillators 58 .…”

Section: Discussionmentioning

confidence: 99%

Fractal basins as a mechanism for the nimble brain

Bollt,

Fish,

Kumar

et al. 2023

Sci Rep

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An interesting feature of the brain is its ability to respond to disparate sensory signals from the environment in unique ways depending on the environmental context or current brain state. In dynamical systems, this is an example of multi-stability, the ability to switch between multiple stable states corresponding to specific patterns of brain activity/connectivity. In this article, we describe chimera states, which are patterns consisting of mixed synchrony and incoherence, in a brain-inspired dynamical systems model composed of a network with weak individual interactions and chaotic/periodic local dynamics. We illustrate the mechanism using synthetic time series interacting on a realistic anatomical brain network derived from human diffusion tensor imaging. We introduce the so-called vector pattern state (VPS) as an efficient way of identifying chimera states and mapping basin structures. Clustering similar VPSs for different initial conditions, we show that coexisting attractors of such states reveal intricately “mingled” fractal basin boundaries that are immediately reachable. This could explain the nimble brain’s ability to rapidly switch patterns between coexisting attractors.

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Section: Discussionmentioning

confidence: 99%

Fractal basins as a mechanism for the nimble brain

Bollt,

Fish,

Kumar

et al. 2023

Sci Rep

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“…Chimera states [1][2][3] , which are paradigmatic for the coexistence of synchronization and desynchronization, can be found even in very small, isolated networks 4,5 . Networks in nature, however, often consist of several interacting layers.…”

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confidence: 99%

Chimera states in multiplex networks: Chameleon-like across-layer synchronization

Andrzejak

Espinoso

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators’ mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups’ position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.

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