Complex partial synchronization patterns in networks of delay-coupled neurons

Nikitin, Denis; Omelchenko, Iryna; Zakharova, Anna; Avetyan, M.; Fradkov, Alexander L.; Schöll, Eckehard

doi:10.1098/rsta.2018.0128

Cited by 34 publications

(24 citation statements)

References 102 publications

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“…Recently, a prominent line of research emerged which studies chimera states in multilayer networks [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Multilayer networks are important modelling tools for complex systems such as transportation networks, social interactions and the brain [58,59].…”

Section: Introductionmentioning

confidence: 99%

Remote pacemaker control of chimera states in multilayer networks of neurons

et al. 2020

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Networks of coupled nonlinear oscillators allow for the formation of nontrivial partially synchronized spatiotemporal patterns, such as chimera states, in which there are coexisting coherent (synchronized) and incoherent (desynchronized) domains. These complementary domains form spontaneously and it is impossible to predict where the synchronized group will be positioned within the network. Therefore, possible ways to control the spatial position of the coherent and incoherent groups forming the chimera states are of high current interest. In this work we investigate how to control chimera patterns in multiplex networks of FitzHugh-Nagumo neurons, and in particular we want to prove that it is possible to remotely control chimera states exploiting the multiplex structure. We introduce a pacemaker oscillator within the network: this is an oscillator that does not receive input from the rest of the network but is sending out information to its neighbours. The pacemakers can be positioned in one or both layers. Their presence breaks the spatial symmetry of the layer in which they are introduced and allows us to control the position of the incoherent domain. We demonstrate how the remote control is possible for both uni-and bidirectional coupling between the layers. Furthermore we show which are the limitations of our control mechanisms when it is generalized from single layer to multilayer networks.

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Section: Introductionmentioning

confidence: 99%

Remote pacemaker control of chimera states in multilayer networks of neurons

et al. 2020

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“…Nikitin et al [15] study partially synchronized solutions in coupled FitzHugh-Nagumo oscillators. The authors found a new regime of coexisting slow and fast oscillations in a twolayer network with identical units, which coexist with chimera states.…”

Section: Content Of the Issuementioning

confidence: 99%

Nonlinear dynamics of delay systems: an overview

Otto

Just

Radons

2019

Phil. Trans. R. Soc. A.

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Time delays play an important role in many fields such as engineering, physics or biology. Delays occur due to finite velocities of signal propagation or processing delays leading to memory effects and, in general, infinite-dimensional systems. Time delay systems can be described by delay differential equations and often include non-negligible nonlinear effects. This overview article introduces the theme issue 'Nonlinear dynamics of delay systems', which contains new fundamental results in this interdisciplinary field as well as recent developments in applications. Fundamentally, new results were obtained especially for systems with time-varying delay and state-dependent delay and for delay system with noise, which do often appear in real systems in engineering and nature. The applications range from climate modelling over network dynamics and laser systems with feedback to human balancing and machine tool chatter.This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

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“…Examples also include air transportation networks, power grids, coupled semiconductor lasers, communication networks, social networks, infectious disease, etc. [1][2][3][4][6][7][8][9] .…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a multiplex neural network with delayed couplings

Mao

Ding

et al. 2021

Appl. Math. Mech.-Engl. Ed.

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Multiplex networks have drawn much attention since they have been observed in many systems, e.g., brain, transport, and social relationships. In this paper, the nonlinear dynamics of a multiplex network with three neural groups and delayed interactions is studied. The stability and bifurcation of the network equilibrium are discussed, and interesting neural activities of the network are explored. Based on the neuron circuit, transfer function circuit, and time delay circuit, a circuit platform of the network is constructed. It is shown that delayed couplings play crucial roles in the network dynamics, e.g., the enhancement and suppression of the stability, the patterns of the synchronization between networks, and the generation of complicated attractors and multi-stability coexistence.

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Complex partial synchronization patterns in networks of delay-coupled neurons

Cited by 34 publications

References 102 publications

Remote pacemaker control of chimera states in multilayer networks of neurons

Remote pacemaker control of chimera states in multilayer networks of neurons

Nonlinear dynamics of delay systems: an overview

Dynamics of a multiplex neural network with delayed couplings

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