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Christian Bick - One of the best experts on this subject based on the ideXlab platform.
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Isotropy of Angular Frequencies and Weak Chimeras with Broken Symmetry
Journal of Nonlinear Science, 2017Co-Authors: Christian BickAbstract:The notion of a weak Chimeras provides a tractable definition for Chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak Chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector—for coupled phase oscillators the angular frequency vector is given by the average of the vector field along a trajectory. Symmetries of solutions automatically imply angular frequency synchronization. We show that the presence of such symmetries is not necessary by giving a result for the existence of weak Chimeras without instantaneous or setwise symmetries for coupled phase oscillators. Moreover, we construct a coupling function that gives rise to chaotic weak Chimeras without symmetry in weakly coupled populations of phase oscillators with generalized coupling.
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Isotropy of Frequencies and Weak Chimeras With Broken Symmetry
arXiv: Dynamical Systems, 2015Co-Authors: Christian BickAbstract:The notion of a weak Chimeras provide a tractable definition for Chimera states in networks of finitely many phase oscillators. Here we rephrase this definition in the language of equivariant dynamical systems: for coupled phase oscillators the notion of a weak Chimera can be cast in terms of the isotropy of the frequency vector-the average of the vector field along a trajectory. While dynamically invariant sets with symmetries are natural candidates for weak Chimeras as nontrivial symmetry immediately implies frequency synchronization, we give a result for the existence of weak Chimeras without instantaneous or setwise symmetries. In particular, we give an explicit example of a coupling function that gives rise to chaotic weak Chimeras without symmetry in weakly coupled populations of phase oscillators with generalized coupling.
Carlo R. Laing - One of the best experts on this subject based on the ideXlab platform.
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Chimera states in networks of phase oscillators the case of two small populations
Physical Review E, 2016Co-Authors: Mark J. Panaggio, Daniel M. Abrams, Peter Ashwin, Carlo R. LaingAbstract:Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, Chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of 2N phase oscillators that are organized in two groups, we find that Chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for N>2 the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that Chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.
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Chimeras in networks of planar oscillators.
Physical Review E, 2010Co-Authors: Carlo R. LaingAbstract:Chimera states occur in networks of coupled oscillators, and are characterized by having some fraction of the oscillators perfectly synchronized, while the remainder are desynchronized. Most Chimera states have been observed in networks of phase oscillators with coupling via a sinusoidal function of phase differences, and it is only for such networks that any analysis has been performed. Here we present the first analysis of Chimera states in a network of planar oscillators, each of which is described by both an amplitude and a phase. We find that as the attractivity of the underlying periodic orbit is reduced Chimeras are destroyed in saddle-node bifurcations, and supercritical Hopf and homoclinic bifurcations of Chimeras also occur.
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Chimera states in heterogeneous networks
Chaos, 2009Co-Authors: Carlo R. LaingAbstract:Chimera states in networks of coupled oscillators occur when some fraction of the oscillators synchronize with one another, while the remaining oscillators are incoherent. Several groups have studied Chimerae in networks of identical oscillators, but here we study these states in heterogeneous models for which the natural frequencies of the oscillators are chosen from a distribution. For a model consisting of two subnetworks, we obtain exact results by reduction to a finite set of differential equations, and for a network of oscillators in a ring, we generalize known results. We find that heterogeneity can destroy Chimerae, destroy all states except Chimerae, or destabilize Chimerae in Hopf bifurcations, depending on the form of the heterogeneity.
Matjaž Perc - One of the best experts on this subject based on the ideXlab platform.
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Chimera states in neuronal networks a review
Physics of Life Reviews, 2019Co-Authors: Soumen Majhi, Dibakar Ghosh, Matjaž Perc, Bidesh K BeraAbstract:Abstract Neuronal networks, similar to many other complex systems, self-organize into fascinating emergent states that are not only visually compelling, but also vital for the proper functioning of the brain. Synchronous spatiotemporal patterns, for example, play an important role in neuronal communication and plasticity, and in various cognitive processes. Recent research has shown that the coexistence of coherent and incoherent states, known as Chimera states or simply Chimeras, is particularly important and characteristic for neuronal systems. Chimeras have also been linked to the Parkinson's disease, epileptic seizures, and even to schizophrenia. The emergence of this unique collective behavior is due to diverse factors that characterize neuronal dynamics and the functioning of the brain in general, including neural bumps and unihemispheric slow-wave sleep in some aquatic mammals. Since their discovery, Chimera states have attracted ample attention of researchers that work at the interface of physics and life sciences. We here review contemporary research dedicated to Chimeras in neuronal networks, focusing on the relevance of different synaptic connections, and on the effects of different network structures and coupling setups. We also cover the emergence of different types of Chimera states, we highlight their relevance in other related physical and biological systems, and we outline promising research directions for the future, including possibilities for experimental verification.
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Nonstationary Chimeras in a neuronal network
EPL, 2018Co-Authors: Zhouchao Wei, Fatemeh Parastesh, Hamed Azarnoush, Sajad Jafari, Dibakar Ghosh, Matjaž Perc, Mitja SlavinecAbstract:Chimeras are special states that are composed of coexisting spatial domains of coherent and incoherent dynamics, which typically emerge in identically coupled oscillators. In this paper, we study a network of nonlocally coupled Hindmarsh-Rose neurons that are subject to an alternating current. We show that Chimera states emerge when the neurons are connected through electrical synapses. The considered model has two coexisting attractors, namely a limit cycle and a chaotic attractor, to which the dynamics converges in dependence on the initial conditions. While earlier research reported the existence of Chimeras in Hindmarsh-Rose neuronal networks mainly through chemical synapses, here we show that an alternating current in an electrically coupled network can also evoke Chimeras, whereby the spatial positions of coherent and incoherent domains vary with time. Remarkably, we also observe Chimera states in locally coupled neurons through electrical synapses, which reduce the relaxation of nonlocallity in the coupling configuration. The existence of nonstationary Chimeras is confirmed by means of a local order parameter.
Anna Zakharova - One of the best experts on this subject based on the ideXlab platform.
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Amplitude Chimeras and Chimera Death in Ring Networks
Understanding Complex Systems, 2020Co-Authors: Anna ZakharovaAbstract:In the present chapter, we discuss special types of Chimera states: amplitude Chimeras and Chimera death. In the intriguing amplitude Chimera regime, coherence-incoherence patterns are formed with respect to the amplitudes only. Chimera death generalizes Chimera patterns to steady states through the death of oscillations. We first describe amplitude Chimeras and Chimera death in the deterministic case without time delay. Further, efficient control mechanisms based on time delay and noise are discussed. In particular, we address the question of how time delay and noise influence the behavior of amplitude Chimera states in ring networks of Stuart-Landau oscillators.
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Coherence-Resonance Chimeras in Ring Networks
Understanding Complex Systems, 2020Co-Authors: Anna ZakharovaAbstract:In the present chapter, we consider noise-induced Chimera patterns called coherence-resonance Chimeras. These peculiar states combine features of coherence resonance and Chimera states and are characterized by the coexistence of two different domains separated in space: one part of the network is spiking coherently in space, while the other exhibits incoherent spiking, i.e., the spiking of neighboring nodes is uncorrelated. We explain the formation mechanism of noise-induced Chimeras and discuss time-delayed feedback control of these patterns. Specifically, we focus on the role of noise and time delay for the Chimera states occurring in ring networks of FitzHugh-Nagumo neurons in the excitable regime.
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Chimera Patterns in Complex Networks
Understanding Complex Systems, 2020Co-Authors: Anna ZakharovaAbstract:This chapter provides a systematic overview of the established results on Chimera states. We begin with a short historical note on how Chimera states have been discovered. Having formulated the existing definitions of Chimera states, we explain their main features. Moreover, we discuss the measures to detect Chimera patterns and give a detailed overview of the systems in which Chimera states have been found. Further, we systematically describe the network topologies for which Chimera patterns have been reported. Then, the types of Chimera states are considered and the existing methods of controlling Chimeras are described. Finally, we give examples of experiments on Chimera states and discuss their main applications.
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Filtering Suppresses Amplitude Chimeras
Frontiers in Applied Mathematics and Statistics, 2019Co-Authors: Tanmoy Banerjee, Anna Zakharova, Biswabibek Bandyopadhyay, Eckehard SchollAbstract:Amplitude Chimera (AC) is an interesting Chimera pattern that has been discovered recently and is distinct from other Chimera patterns, like phase Chimeras and amplitude mediated phase Chimeras. Unlike other Chimeras, in the AC pattern all the oscillators have the same phase velocity, however, the oscillators in the incoherent domain show periodic oscillations with randomly shifted origin. In this paper we investigate the effect of local filtering in the coupling path on the occurrence of AC patterns. Our study is motivated by the fact that in the practical coupling channels filtering effects come into play due to the presence of dispersion and dissipation. We show that a low-pass or all-pass filtering is actually detrimental to the occurrence of AC. We quantitatively establish that with decreasing cut-off frequency of the filter, an AC transforms into a synchronized pattern. We also show that the symmetry-breaking steady state, i.e., the oscillation death state can be revoked and rhythmogenesis can be induced by local filtering. Our study will shed light on the understanding of many biological systems where spontaneous symmetry-breaking and local filtering occur simultaneously.
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Noise-Induced Chimera States in a Neural Network
Patterns of Dynamics, 2017Co-Authors: Anna Zakharova, Nadezhda Semenova, Vadim S. Anishchenko, Eckehard SchollAbstract:We show that Chimera patterns can be induced by noise in nonlocally coupled neural networks in the excitable regime. In contrast to classical Chimeras, occurring in noise-free oscillatory networks, they have features of two phenomena: coherence resonance and Chimera states. Therefore, we call them coherence-resonance Chimeras. These patterns demonstrate the constructive role of noise and appear for intermediate values of noise intensity, which is a characteristic feature of coherence resonance. In the coherence-resonance Chimera state a neural network of identical elements splits into two coexisting domains with different behavior: spatially coherent and spatially incoherent, a typical property of Chimera states. Moreover, these noise-induced Chimera states are characterized by alternating behavior: coherent and incoherent domains switch periodically their location. We show that this alternating switching can be explained by analyzing the coupling functions.
G. L. Andersen - One of the best experts on this subject based on the ideXlab platform.
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Greengenes, a Chimera-checked 16S rRNA gene database and workbench compatible with ARB
Applied and Environmental Microbiology, 2006Co-Authors: Todd Z Desantis, Timo Huber, Daniel Dalevi, M Rojas, N. Larsen, Philip Hugenholtz, K. Keller, P Hu, Eoin L Brodie, G. L. AndersenAbstract:A 16S rRNA gene database (http://greengenes.lbl.gov) addresses limitations of public repositories by providing Chimera screening, standard alignment, and taxonomic classification using multiple published taxonomies. It was found that there is incongruent taxonomic nomenclature among curators even at the phylum level. Putative Chimeras were identified in 3% of environmental sequences and in 0.2% of records derived from isolates. Environmental sequences were classified into 100 phylum-level lineages in the Archaea and Bacteria.