Weak multiplexing induces coherence resonance

Semenova, Nadezhda; Zakharova, Anna

doi:10.1063/1.5037584

Cited by 59 publications

(58 citation statements)

References 49 publications

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“…As we mentioned earlier, it has been shown in [45] with another version of the FHN neuron model that stronger coupling forces rather shift the CV -curve to lower values, thus enhancing CR. The version of the FHN neuron model used here is more general than that in [45] (see also [27] which uses the same version as in [45]) and shows a rather opposite effect, i.e., stronger coupling forces deteriorate CR. The reason behind this difference lies in the details of the equations of the two versions used.…”

Section: Coherence Resonancementioning

confidence: 64%

“…Therefore, increasing the coupling force tends to bring their version of the FHN model closer to the bifurcation threshold, thus enhancing CR. In the current paper, only the slow variable equation of the neurons is different from that in [27] and [45], but one can already see in Fig.1(a) that increasing the strength of the coupling force and the length of the time delay within some interval does not switch the network out of the excitable regime. As the coupling force be-comes stronger and the time delay longer, the network tends to move rather further away from the oscillatory regime, i.e., away from the Hopf bifurcation threshold.…”

Section: Coherence Resonancementioning

confidence: 66%

“…But one should note that the response of CR to changes in time-delayed coupling can vary from one kind of nonlinear oscillator to another depending on the details of the equation. That is, there is no general behavior as stronger coupling forces may strengthen CR in a network of one kind of nonlinear oscillators [45], but as we shall see in the current paper, it can instead weaken CR in a network of just slightly modified equations of the nonlinear oscillators. Therefore, without investigations, one cannot say a priori how CR will behave in response to changes in time-delayed couplings in a network of a particular nonlinear oscillator, even if this behavior is known for a network of another nonlinear oscillator, with a slightly modified equation.…”

Section: Coherence Resonancementioning

confidence: 77%

“…As the coupling force be-comes stronger and the time delay longer, the network tends to move rather further away from the oscillatory regime, i.e., away from the Hopf bifurcation threshold. In Fig.2(c), we even see that strong coupling and long time delays can switch the network from an oscillatory regime into a delayed-coupling-induced excitable regime; this effect is the exact opposite of that produced by the model used in [27] and [45]. In general, the further away we are from the (Hopf or saddle-node) bifurcation threshold, the more difficult it is for CR to occur.…”

Section: Coherence Resonancementioning

confidence: 86%

See 3 more Smart Citations

Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network

Yamakou

Jost

2019

Phys. Rev. E

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We consider a two-layer multiplex network of diffusively coupled FitzHugh-Nagumo (FHN) neurons in the excitable regime. We show that the phenomenon of coherence resonance (CR) in one layer cannot only be controlled by the network topology, the intra and inter-layer time-delayed couplings, but also by another phenomenon, namely, self-induced stochastic resonance (SISR) in the other layer. Numerical computations show that when the layers are isolated, each of these noise-induced phenomena is weakened (strengthened) by a sparser (denser) ring network topology, stronger (weaker) intra-layer coupling forces, and longer (shorter) intra-layer time delays. However, CR shows a much higher sensitivity than SISR to changes in these control parameters. It is also shown, in contrast to SISR in a single isolated FHN neuron, that the maximum noise amplitude at which SISR occurs in the network of coupled FHN neurons is controllable, especially in the regime of strong coupling forces and long time delays. In order to use SISR in the first layer of the multiplex network to control CR in the second layer, we first choose the control parameters of the second layer in isolation such that in one case CR is poor and in another case, non-existent. It is then shown that a pronounced SISR cannot only significantly improve a poor CR, but can also induce a pro-

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Section: Coherence Resonancementioning

confidence: 64%

Section: Coherence Resonancementioning

confidence: 66%

Section: Coherence Resonancementioning

confidence: 77%

Section: Coherence Resonancementioning

confidence: 86%

See 2 more Smart Citations

Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network

Yamakou

Jost

2019

Phys. Rev. E

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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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Introduction

Berner

2021

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

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Weak multiplexing induces coherence resonance

Cited by 59 publications

References 49 publications

Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network

Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

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