Chimeras in Multiplex Networks: Interplay of Inter- and Intra-Layer Delays

Sawicki, Jakub; Ghosh, Saptarshi; Jalan, Sarika; Zakharova, Anna

doi:10.3389/fams.2019.00019

Cited by 26 publications

(19 citation statements)

References 46 publications

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“…Their use in the optimization and control of dynamical behaviors have therefore attracted much attention recently. The multiplexing of networks has been shown to control many dynamical behaviors in neural networks, including synchronization (Gambuzza et al, 2015 ; Singh et al, 2015 ; Andrzejak et al, 2017 ; Leyva et al, 2017 ; Zhang et al, 2017 ), pattern formation (Kouvaris et al, 2015 ; Ghosh and Jalan, 2016 ; Ghosh et al, 2016 , 2018 ; Maksimenko et al, 2016 ; Bera et al, 2017 ; Bukh et al, 2017 ), solitary waves (Mikhaylenko et al, 2019 ), and chimera states (Panaggio and Abrams, 2015 ; Schöll, 2016 ; Ghosh et al, 2018 , 2019 ; Omelchenko et al, 2018 ; Sawicki et al, 2019 ). Chimera states are synchronization patterns occurring in symmetric networks (on average), characterized by the coexistence of varying synchronization levels side-by-side.…”

Section: Introductionmentioning

confidence: 99%

Optimal Self-Induced Stochastic Resonance in Multiplex Neural Networks: Electrical vs. Chemical Synapses

Yamakou

Hjorth

Martens

2020

Front. Comput. Neurosci.

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Electrical and chemical synapses shape the dynamics of neural networks, and their functional roles in information processing have been a longstanding question in neurobiology. In this paper, we investigate the role of synapses on the optimization of the phenomenon of self-induced stochastic resonance in a delayed multiplex neural network by using analytical and numerical methods. We consider a two-layer multiplex network in which, at the intra-layer level, neurons are coupled either by electrical synapses or by inhibitory chemical synapses. For each isolated layer, computations indicate that weaker electrical and chemical synaptic couplings are better optimizers of self-induced stochastic resonance. In addition, regardless of the synaptic strengths, shorter electrical synaptic delays are found to be better optimizers of the phenomenon than shorter chemical synaptic delays, while longer chemical synaptic delays are better optimizers than longer electrical synaptic delays; in both cases, the poorer optimizers are, in fact, worst. It is found that electrical, inhibitory, or excitatory chemical multiplexing of the two layers having only electrical synapses at the intra-layer levels can each optimize the phenomenon. Additionally, only excitatory chemical multiplexing of the two layers having only inhibitory chemical synapses at the intra-layer levels can optimize the phenomenon. These results may guide experiments aimed at establishing or confirming to the mechanism of self-induced stochastic resonance in networks of artificial neural circuits as well as in real biological neural networks.

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Section: Introductionmentioning

confidence: 99%

Optimal Self-Induced Stochastic Resonance in Multiplex Neural Networks: Electrical vs. Chemical Synapses

Yamakou

Hjorth

Martens

2020

Front. Comput. Neurosci.

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“…[25][26][27] Moreover, the phenomenon of relay synchronization might be associated with an enhancement of synchronization in complex networks with heterogeneous units. 27 Recently, relay synchronization has also been demonstrated in remote pairs of layers, 6,7,[28][29][30] where in Ref. 6 complex topologies like Erdös-Renyi and scale-free were studied.…”

Section: Article Scitationorg/journal/chamentioning

confidence: 99%

Effect of topology upon relay synchronization in triplex neuronal networks

Drauschke

Sawicki

Berner

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Relay synchronization in complex networks is characterized by the synchronization of remote parts of the network due to their interaction via a relay. In multilayer networks, distant layers that are not connected directly can synchronize due to signal propagation via relay layers. In this work, we investigate relay synchronization of partial synchronization patterns like chimera states in three-layer networks of interacting FitzHugh-Nagumo oscillators. We demonstrate that the phenomenon of relay synchronization is robust to topological random inhomogeneities of small-world type in the layer networks. We show that including randomness in the connectivity structure either of the remote network layers or of the relay layer increases the range of interlayer coupling strength where relay synchronization can be observed.

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“…In such scenarios, the multiplex (multilayer) framework turns out to be an apt contender in representing different dynamical processes acting on the same set of units through different layers comprising different genres of links having different connectivity among the same set of interlinked nodes [33][34][35]. Recently, the investigations pertaining to the emergence of chimera states and solitary states have been extended to multilayer networks subjected to a variety of dynamical models [36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Assisted Chimera and Solitary States in Networks

et al. 2021

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Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial systems. It has been further demonstrated that such states can be engineered in systems of coupled oscillators by suitable implementation of communication delays. Here, using supervised machine learning, we predict (a) the precise value of delay which is sufficient for engineering chimera and solitary states for a given set of system's parameters, as well as (b) the intensity of incoherence for such engineered states. Ergo, using few initial data points we generate a machine learning model which can then create a more refined phase plot as well as by including new parameter values. We demonstrate our results for two different examples consisting of single layer and multi layer networks. First, the chimera states (solitary states) are engineered by establishing delays in the neighboring links of a node (the interlayer links) in a 2-D lattice (multiplex network) of oscillators. Then, different machine learning classifiers, K-nearest neighbors (KNN), support vector machine (SVM) and multi-layer perceptron neural network (MLP-NN) are employed by feeding the data obtained from the network models. Once a machine learning model is trained using the limited amount of data, it predicts the precise value of critical delay as well as the intensity of incoherence for a given unknown systems parameters values. Testing accuracy, sensitivity, and specificity analysis reveal that MLP-NN classifier is better suited than Knn or SVM classifier for the predictions of parameters values for engineered chimera and solitary states. The technique provides an easy methodology to predict critical delay values as well as intensity of incoherence for that delay value for designing an experimental setup to create solitary and chimera states.

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Chimeras in Multiplex Networks: Interplay of Inter- and Intra-Layer Delays

Cited by 26 publications

References 46 publications

Optimal Self-Induced Stochastic Resonance in Multiplex Neural Networks: Electrical vs. Chemical Synapses

Optimal Self-Induced Stochastic Resonance in Multiplex Neural Networks: Electrical vs. Chemical Synapses

Effect of topology upon relay synchronization in triplex neuronal networks

Machine Learning Assisted Chimera and Solitary States in Networks

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