☆ 4.7 Review

Chimeras in globally coupled oscillators: A review

CHAOS (2023)

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Article Mathematics, Interdisciplinary Applications

Critical visit to the chimera world

M. A. Ferre

Summary: Chimera states refer to a spatiotemporal phenomenon where coherence and incoherence dynamics coexist in homogeneous systems. Originally observed in non-locally coupled phase oscillators, this phenomenon has been observed in various systems including chaotic maps, time-delay systems, and complex networks. This review summarizes the different systems where chimera states are observed, focusing on theoretical and experimental contributions. It also critically examines the definitions of chimera states and presents some related works. Furthermore, new research perspectives are suggested due to the stage of the field.

CHAOS SOLITONS & FRACTALS (2023)

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Article Physics, Fluids & Plasmas

Multistable chimera states in a smallest population of three coupled oscillators

A. Ragavan et al.

Summary: We have observed the emergence of distinct multistable chimera states, in addition to chimera death and synchronized states, in a smallest population of three globally coupled oscillators with mean-field diffusive coupling. A series of torus bifurcations result in the manifestation of distinct periodic orbits, leading to the creation of chimera states with two synchronized oscillators coexisting with an asynchronous oscillator. Subsequent Hopf bifurcations lead to homogeneous and inhomogeneous steady states, resulting in desynchronized steady states and chimera death state among the coupled oscillators. The stability of periodic orbits and steady states is lost through a sequence of saddle-loop and saddle-node bifurcations, ultimately resulting in a stable synchronized state. We have also extended these findings to N coupled oscillators and derived the variational equations corresponding to perturbation transverse to the synchronization manifold, confirming the synchronized state in the two-parameter phase diagrams using its largest eigenvalue. Chimera states in three coupled oscillators emerge as a solitary state in N coupled oscillator ensemble.

PHYSICAL REVIEW E (2023)

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Article Neurosciences

Chimera states and cluster solutions in Hindmarsh-Rose neural networks with state resetting process

Yi Yang et al.

Summary: The neural state resetting model integrates neuronal system with state resetting process to generate new firing patterns and irregular limit cycles. Chimera and cluster states are discussed in Hindmarsh-Rose neural networks with state resetting process, focusing on synchronization phenomena. By improving chimera measures and analyzing phase diagrams, time series diagrams, and probability density histograms, the study enriches the firing mode of the neural networks with state resetting process.

COGNITIVE NEURODYNAMICS (2022)

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Article Mathematics, Applied

Mixed-mode chimera states in pendula networks

P. Ebrahimzadeh et al.

Summary: We report the emergence of peculiar chimera states in networks of identical pendula with global phase-lagged coupling. These mixed-mode chimeras may be interpreted as images of bump states known in neuroscience in the context of modeling the working memory. Through simulations and analysis of pendulum networks of different sizes, we identified five characteristic types of system behavior.

CHAOS (2022)

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Article Mathematics, Interdisciplinary Applications

Multiplexing noise induces synchronization in multilayer networks

E. Rybalova et al.

Summary: We numerically studied the spatio-temporal behavior of a two-layer multiplex network with modulated interlayer coupling noise. Our research found that low-frequency multiplexing noise can generate solitary states in the network and reveal the special temporal dynamics of these solitary nodes. Furthermore, it was discovered that complete and near-complete synchronization between layers can be achieved under certain noise characteristics.

CHAOS SOLITONS & FRACTALS (2022)

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Article Multidisciplinary Sciences

Multistability and anomalies in oscillator models of lossy power grids

Robin Delabays et al.

Summary: The analysis of dissipatively coupled oscillators in power grids is challenging but relevant. This study establishes a close correspondence between stable synchronous states and the winding partition of the state space, providing a geometric framework for computing synchronous solutions. It is shown that loop flows and dissipation can have counterintuitive effects on the system's transfer capacity and multistability. The proposed geometric framework is applied to calculate power flows in the IEEE RTS-96 test system, identifying high voltage solutions with distinct loop flows.

NATURE COMMUNICATIONS (2022)

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Article Mathematics, Applied

Extreme events in a complex network: Interplay between degree distribution and repulsive interaction

Arnob Ray et al.

Summary: The role of topological heterogeneity in the origin of extreme events in a network is investigated. High degree nodes are vulnerable to weak repulsive interactions, while low degree nodes are susceptible to strong interactions. The occurrence of extreme events depends on the interplay between topological heterogeneity and repulsive interaction, and the formation position of extreme events shifts from high degree nodes to low degree nodes as the strength of repulsive interaction increases.

CHAOS (2022)

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Article Physics, Fluids & Plasmas

Solitary routes to chimera states

Leonhard Schuelen et al.

Summary: This study demonstrates through numerical analysis how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states, exhibiting extensive chaos in large systems.

PHYSICAL REVIEW E (2022)

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Article Physics, Fluids & Plasmas

Nonequilibrium thermodynamic characterization of chimeras in a continuum chemical oscillator system

Premashis Kumar et al.

Summary: This study investigates the emergence of the chimera state in a continuum chemical oscillator system using a complex Ginzburg-Landau equation. The study systematically examines the evolution of nonequilibrium thermodynamic entities associated with the chimera state. The temporal evolution of the entropy production rate exhibits beat patterns in the frequency domain, while symmetric profiles associated with the incoherent regime appear in descriptions of the chimera's dynamics and thermodynamics. The study highlights the guiding role of the information uncertainty principle in shaping the energetics of the chimera.

PHYSICAL REVIEW E (2022)

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Article Physics, Fluids & Plasmas

Emerging chimera states under nonidentical counter-rotating oscillators

K. Sathiyadevi et al.

Summary: This study explores the importance of frequency in the coexisting corotating and counter-rotating systems. The researchers found that the dynamical states of the system do not preserve symmetry and revealed a transition from incoherent mixed synchronization to coherent mixed synchronization through a chimera state. They also discovered that partial symmetry breaking exists due to the coexistence of symmetry-preserving and symmetry-breaking behavior in the initial state space.

PHYSICAL REVIEW E (2022)

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Article Physics, Multidisciplinary

Scroll ring chimera states in oscillatory networks

Volodymyr Maistrenko et al.

Summary: The study demonstrates the appearance of scroll ring and scroll toroid chimera states in the Kuramoto model of coupled phase oscillators in the 3D grid topology with inertia. The proposed initial conditions allow for obtaining both single and multiple scroll ring and toroid chimeras with different diameters. These patterns can coexist with solitary states and patterns in the oscillatory networks.

JOURNAL OF PHYSICS COMMUNICATIONS (2021)

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Article Physics, Multidisciplinary

Mechanism for Strong Chimeras

Yuanzhao Zhang et al.

Summary: The study shows that many stable chimera states arise because coherence in part of the system is sustained by incoherence in the rest of the system, which can be considered as a deterministic analog of noise-induced synchronization and is shown to underlie the emergence of strong chimeras. This mechanism offers a new interpretation that chimeras are a natural link between coherence and incoherence.

PHYSICAL REVIEW LETTERS (2021)

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Article Multidisciplinary Sciences

Between synchrony and turbulence: intricate hierarchies of coexistence patterns

Sindre W. Haugland et al.

Summary: The text explores the behaviors of coupled oscillators, including synchronization and incoherence, as well as the discovery of "chimera states" and their relationship with synchronization and asynchronization. It demonstrates that globally coupled identical oscillators can express a wider range of coexistence patterns, including chimeras.

NATURE COMMUNICATIONS (2021)

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Article Mathematics, Interdisciplinary Applications

Interplay between solitary states and chimeras in multiplex neural networks

E. V. Rybalova et al.

Summary: In this study, we numerically investigated the spatiotemporal dynamics and synchronization of a heterogeneous two-layer multiplex network consisting of FitzHugh-Nagumo neurons. We found competitive behavior between solitary states and chimeras in the transition to synchronous regime with the introduction of interlayer coupling. By using different types of interlayer coupling, we systematically studied synchronization between different layers.

CHAOS SOLITONS & FRACTALS (2021)

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Article Physics, Fluids & Plasmas

Explosive synchronization and chimera in interpinned multilayer networks

Ajay Deep Kachhvah et al.

Summary: The study found that in multilayer and multiplexed networks, a multilayer network constructed by setting up all-to-all interlayer connections can lead to explosive synchronization in the two populations, while a multiplex formation with only mirror nodes interconnected supports simultaneous explosive transitions in the two populations. Both explosive synchronization and chimera phenomena are supported by rigorous theoretical mean-field analysis in the presence of random pinning in interlayer interactions.

PHYSICAL REVIEW E (2021)

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Review Mathematics, Interdisciplinary Applications

The changing notion of chimera states, a critical review

Sindre W. Haugland

Summary: Chimera states, characterized by the coexistence of synchronous and asynchronous motion, have been extensively researched since 2004. Different model types and coupling schemes have influenced the common understanding of what constitutes a chimera state, with various chimera-derived terms emerging over the years.

JOURNAL OF PHYSICS-COMPLEXITY (2021)

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Article Physics, Fluids & Plasmas

Connecting minimal chimeras and fully asymmetric chaotic attractors through equivariant pitchfork bifurcations

Sindre W. Haugland et al.

Summary: Highly symmetric networks can exhibit partly symmetry-broken states, including clusters and chimera states. The study of four globally coupled Stuart-Landau oscillators revealed interconnected solutions with different symmetries, including chaotic minimal chimeras and fully asymmetric chaotic states. Equivariant pitchfork bifurcations mediate between these cascades, leading to equivariant pitchforks of chaotic attractors.

PHYSICAL REVIEW E (2021)

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Article Physics, Fluids & Plasmas

Chimera complexity

Serhiy Brezetsky et al.

Summary: This study reveals the complex behavior of chimeras in small networks of phase oscillators with inertia, exhibiting extreme sensitivity to initial conditions and parameter changes. The unpredictability of the system dynamics, characterized by heteroclinic switching and riddling basins of attractions, poses a challenge in the field of network sciences. The presence of stable phase-locked states or other stable chimeras in the system further adds to the uncertainty in its behavior.

PHYSICAL REVIEW E (2021)

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Review Mathematics, Applied

Neuron-like spiking and bursting in Josephson junctions: A review

Arindam Mishra et al.

Summary: Researchers have observed similarities between the spiking and bursting behaviors of superconducting Josephson junctions with that of neurons. Recent studies have also shown similar neuronal functional behavior in superconducting nanowires. The history of this research highlights the origins and dynamic interpretations of these phenomena.

CHAOS (2021)

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Article Physics, Fluids & Plasmas

Chimeralike states in a minimal network of active camphor ribbons

Jyoti Sharma et al.

Summary: The study demonstrates the existence of chimeralike states in an ensemble of homogeneous coupled oscillators, specifically in active camphor ribbons. These states are characterized by the coexistence of synchronized and unsynchronized groups within the ensemble. The experimental results were successfully reproduced using a numerical model simulating the repulsive Yukawa interactions between the ribbons.

PHYSICAL REVIEW E (2021)

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Article Multidisciplinary Sciences

Network-induced multistability through lossy coupling and exotic solitary states

Frank Hellmann et al.

NATURE COMMUNICATIONS (2020)

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

Joydeep Singha et al.

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Symmetry breaking by power-law coupling

Biswabibek Bandyopadhyay et al.

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Symmetry breaking-induced state-dependent aging and chimera-like death state

I Gowthaman et al.

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Extreme events in a network of heterogeneous Josephson junctions

Arnob Ray et al.

PHYSICAL REVIEW E (2020)

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Review Biology

Chimera states in neuronal networks: A review

Soumen Majhi et al.

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Cluster singularity: The unfolding of clustering behavior in globally coupled Stuart-Landau oscillators

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Dynamics and stability of chimera states in two coupled populations of oscillators

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Lyapunov spectra and collective modes of chimera states in globally coupled Stuart-Landau oscillators

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Chimera States in Ecological Network Under Weighted Mean-Field Dispersal of Species

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Asymmetric cluster and chimera dynamics in globally coupled systems

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Christian Bick et al.

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Arindam Mishra et al.

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Yuri Maistrenko et al.

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Amplitude-phase coupling drives chimera states in globally coupled laser networks

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Azamat Yeldesbay et al.

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Louis M. Pecora et al.

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Tomasz Kapitaniak et al.

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