Non-identical multiplexing promotes chimera states

Ghosh, Saptarshi; Zakharova, Anna; Jalan, Sarika

doi:10.1016/j.chaos.2017.11.010

Cited by 46 publications

(34 citation statements)

References 33 publications

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“…In particular, the impact of strong multiplexing, when the strength of the coupling between the layers is comparable with that inside each layer, has been investigated for coupled chaotic maps 33,34 . In more detail, it has been shown that strong multiplexing can be used to control chimeras in networks of coupled chaotic maps 34 . The impact of strong multiplexing with an uncoupled layer has been investigated for a network of Hindmarsh-Rose neurons in 35 , where the strong inter-layer links represent chemical connections and weak intra-layer couplings model electrical synapses.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, in the case of the multilayer brain network, physical connections may be adjustable while the manipulation of the functional connectivity is much more complicated. Although the phenomenon of synchronization 30,[38][39][40][41] and formation of partial synchronization patterns [28][29][30][31]33,34,[42][43][44] have been recently considered in multilayer networks, the challenging problem of controlling chimeras by weak multiplexing, in particular, in neuronal networks has not been yet investigated.…”

Section: Introductionmentioning

confidence: 99%

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Weak multiplexing in neural networks: Switching between chimera and solitary states

Mikhaylenko

Ramlow

Jalan

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate spatio-temporal patterns occurring in a two-layer multiplex network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the coupling between the layers is smaller than that within the layers, can have a significant impact on the dynamics of the neural network. We develop control strategies based on weak multiplexing and demonstrate how the desired state in one layer can be achieved without manipulating its parameters, but only by adjusting the other layer. We find that for coupling range mismatch weak multiplexing leads to the appearance of chimera states with different shapes of the mean velocity profile for parameter ranges where they do not exist in isolation. Moreover, we show that introducing a coupling strength mismatch between the layers can suppress chimera states with one incoherent domain (one-headed chimeras) and induce various other regimes such as in-phase synchronization or two-headed chimeras. Interestingly, small intra-layer coupling strength mismatch allows to achieve solitary states throughout the whole network.In nonlinear dynamics the paradigmatic FitzHugh-Nagumo (FHN) system is used to model the behavior of neurons. A single-layer network of nonlocally coupled oscillatory FHN neurons demonstrates various dynamic regimes including chimera states, that represent an intriguing mechanism of transition from complete coherence to complete incoherence. Here, we focus on a two-layer multiplex network and develop the tools for controlling the spatio-temporal patterns in the presence of weak coupling between the layers, i.e. weak multiplexing. We show that multiplexing combined with a mismatch between the layers, allows to induce chimera states in networks, where they do not appear in isolation. Our control also works in the opposite direction leading to the suppression of chimera states. Interestingly, small mismatch in the intra-layer coupling strength results in the formation of solitary states, that offer, compared to chimera states, an alternative scenario of transition from coherence to incoherence. Since multilayer structures naturally occur in neural networks (e.g., brain networks), we expect that our results can be useful for understanding and controlling of biological networks.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Weak multiplexing in neural networks: Switching between chimera and solitary states

Mikhaylenko

Ramlow

Jalan

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…One of an inexhaustible area of research is connected with nonlinear ensembles with a large number of elements and different network topologies, which give rise to various types of spatiotemporal dynamics. Thus, besides widely considered chimera states (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12]), ensembles with nonlocal coupling can demonstrate another, recently found spatio-temporal structure, which is called "solitary state" [7-9, 11, 13-21]. In contrast to the chimera state (which consists of spatially divided clusters of coherent and incoherent behaviour), the solitary state regime is characterized by a coherent behaviour of the whole system, except several elements.…”

Section: Introductionmentioning

confidence: 99%

Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps

Semenova

Вадивасова

Анищенко

2018

Eur. Phys. J. Spec. Top.

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We study the peculiarities of the solitary state appearance in the ensemble of nonlocally coupled chaotic maps. We show that nonlocal coupling and features of the partial elements lead to arising of multistability in the system. The existence of solitary state is caused by formation of two attractive sets with different basins of attraction. Their basins are analysed depending on coupling parameters.

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“…In neuroscience, multilayer networks represent for instance neurons in different areas of the brain, neurons connected either by a chemical link or by an electrical synapsis, or the modular connectivity structure of brain regions [43][44][45][46][47][48][49][50][51]. A special case of multilayer networks are multiplex topologies, where each layer contains the same set of nodes, and only pairwise connections between corresponding nodes from neighbouring layers exist [52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71].In spite of the lively interest in the topic of adaptive networks, little is known about the interplay of adaptively coupled groups of networks [25,72,73]. Such adaptive multilayer or multiplex networks appear naturally in neuronal networks, e.g., in interacting neuron populations with plastic synapses but different plasticity rules within each population [74,75], or affected by different mechanisms of plasticity [76], or the transport of metabolic resources [77].…”

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confidence: 99%

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

2020

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We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuro-and social sciences, as well as biology, engineering, and other disciplines. We show by theoretical analysis and computer simulations that multiplexing in a multi-layer network with symmetry can induce various stable phase cluster states in a situation where they are not stable or do not even exist in the single layer. Further, we develop a method for the analysis of Laplacian matrices of multiplex networks which allows for insight into the spectral structure of these networks enabling a reduction to the stability problem of single layers. We employ the multiplex decomposition to provide analytic results for the stability of the multilayer patterns. As local dynamics we use the paradigmatic Kuramoto phase oscillator, which is a simple generic model and has been successfully applied in the modeling of synchronization phenomena in a wide range of natural and technological systems.Complex networks are an ubiquitous paradigm in nature and technology, with a wide field of applications ranging from physics, chemistry, biology, neuroscience, to engineering and socio-economic systems. Of particular interest are adaptive networks, where the connectivity changes in time, for instance, the synaptic connections between neurons are adapted depending on the relative timing of neuronal spiking [1][2][3][4][5]. Similarly, chemical systems have been reported [6], where the reaction rates adapt dynamically depending on the variables of the system. Activity-dependent plasticity is also common in epidemics [7] and in biological or social systems [8]. Synchronization is an important feature of the dynamics in networks of coupled nonlinear oscillators [9][10][11][12][13]. Various synchronization patterns are known, like cluster synchronization where the network splits into groups of synchronous elements [14], or partial synchronization patterns like chimera states where the system splits into coexisting domains of coherent (synchronized) and incoherent (desynchronized) states [15][16][17]. These patterns were also explored in adaptive networks [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Furthermore, adapting the network topology has also successfully been used to control cluster synchronization in delay-coupled networks [34].Another focus of recent research in network science are multilayer networks, which are systems interconnected through different types of links [35][36][37][38]. A prominent example are social networks which can be described as groups of people with different patterns of contacts or interactions between them [39][40][41]. Other applications are communication, supply, and transportation networks, for instance power grids, subway networks, or airtraffic networks [42]. In neuroscience, multilayer networks represent for instance neurons in different areas of the brain, neurons connected either by a chemical link or by an electrical synapsis, or...

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Non-identical multiplexing promotes chimera states

Cited by 46 publications

References 33 publications

Weak multiplexing in neural networks: Switching between chimera and solitary states

Weak multiplexing in neural networks: Switching between chimera and solitary states

Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

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