Effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks

Sun, Xiaojuan; Perc, Matjaž; Kurths, Jürgen

doi:10.1063/1.4983838

Cited by 87 publications

(17 citation statements)

References 54 publications

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“…Time delay in nonlinear systems has been recognized as an important factor affecting various dynamics [34,35]. Multistability is one of the most interesting properties in dynamic systems.…”

Section: Resultsmentioning

confidence: 99%

Multiple bifurcations and periodic coexistence in a delayed Hopfield two-neural system with a monotonic activation function

et al. 2019

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In this paper, we consider a delayed Hopfield two-neural system with a monotonic activation function and find the periodic coexistence by bifurcation analysis. Firstly, we obtain the pitchfork bifurcation of the trivial equilibrium employing the central manifold and normal form methods. The neural system exhibits two pitchfork bifurcations near the trivial equilibrium. Then, analyzing the characteristic equation of the nontrivial equilibrium, we illustrate the saddle-node bifurcation of the nontrivial equilibria. The system exhibits the multi-coexistences of the stable and unstable equilibria. Further, we illustrate the plane regions of parameters having different numbers of equilibria. To obtain a time delay in neural system dynamics, we present the stability analysis and find the periodic orbit. The system exhibits stability switching by the Hopf bifurcation curves. Finally, the dynamic behaviors near the Hopf-Hopf bifurcation point are presented. The system exhibits coexistence of multiple periodic orbits with different frequencies.

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“…Time delay in nonlinear systems has been recognized as an important factor affecting various dynamics [34,35]. Multistability is one of the most interesting properties in dynamic systems.…”

Section: Resultsmentioning

confidence: 99%

Multiple bifurcations and periodic coexistence in a delayed Hopfield two-neural system with a monotonic activation function

et al. 2019

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“…Content may change prior to final publication. networks [4][5][6][7][8][9][10][11][12][13][14][15]. The relevant literature shows that the main factors affecting the synchronization of coupled neuronal networks are the network topology [4][5][6][7][8], time delay in the network [9,10], coupling strength [11][12][13][14], and multilayer network structure [15], etc.…”

Section: Introductionmentioning

confidence: 99%

The Synchronization Behaviors of Memristive Synapse-Coupled Fractional-Order Neuronal Networks

Yang

Zhang

2021

IEEE Access

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The synchronization behaviors of memristive synapse-coupled fractional-order neuronal networks are investigated in this paper. Based on the integer-order memristive synapse-coupled neuronal network, a fractional-order model is proposed, and a ring network composed of fractional-order memristive synapse-coupled neuronal subnetworks is constructed. Then, the synchronization behaviors of two fractional-order memristive synapse-coupled neurons and the ring fractional-order memristive synapsecoupled neuronal network are discussed numerically. These research results suggest several novel phenomena and allow several conclusions to be drawn. For the two coupled neurons, different fractionalorders can change the threshold of memristive synapse parameter 1 k when the two neurons are in perfect synchronization. The synchronization transitions are affected by the fractional-order and memristive synapse. Different from the integer-order model, perfect synchronization can occur before phase synchronization for some fractional-orders. Under a certain external current intensity, the transition between periodic synchronization and chaotic synchronization occurs as the fractional-order changes. The chaotic synchronization range is larger because of the memristive synapse. For the ring neuronal network coupled subnetworks, the results illustrate that the collective behaviors including incoherent, coherent, and chimera states can be induced by the fractional-order. In addition, the network's synchronization degree is influenced by the fractional-order. The synchronization transition of the neuronal network also occurs with changes in the fractional-order.

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“…Many dynamical systems, both natural and man-made, are composed of interacting parts. Examples include Josephson junctions [1,2], neuronal networks [3][4][5], the cardiorespiratory system [6][7][8], cardiorespiratory-brain interactions [9][10][11][12], and systems occurring in social sciences [13,14], communications [15,16] and chemistry [17][18][19]. Such systems often have external influences leading to time-variability in their mathematical description, e.g.…”

Section: Introductionmentioning

confidence: 99%

Synchronization transitions caused by time-varying coupling functions

Hagos

Stankovski

Newman

et al. 2019

Phil. Trans. R. Soc. A.

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Interacting dynamical systems are widespread in nature. The influence that one such system exerts on another is described by a coupling function; and the coupling functions extracted from the time-series of interacting dynamical systems are often found to be time-varying. Although much effort has been devoted to the analysis of coupling functions, the influence of time-variability on the associated dynamics remains largely unexplored. Motivated especially by coupling functions in biology, including the cardiorespiratory and neural delta-alpha coupling functions, this paper offers a contribution to the understanding of effects due to time-varying interactions. Through both numerics and mathematically rigorous theoretical consideration, we show that for time-variable coupling functions with time-independent net coupling strength, transitions into and out of phase- synchronization can occur, even though the frozen coupling functions determine phase-synchronization solely by virtue of their net coupling strength. Thus the information about interactions provided by the shape of coupling functions plays a greater role in determining behaviour when these coupling functions are time-variable.This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

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Effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks

Cited by 87 publications

References 54 publications

Multiple bifurcations and periodic coexistence in a delayed Hopfield two-neural system with a monotonic activation function

Multiple bifurcations and periodic coexistence in a delayed Hopfield two-neural system with a monotonic activation function

The Synchronization Behaviors of Memristive Synapse-Coupled Fractional-Order Neuronal Networks

Synchronization transitions caused by time-varying coupling functions

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