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Stability, bifurcations and synchronization in a delayed neural network model of n-identical neurons

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  • Kundu, Amitava
  • Das, Pritha
  • Roy, A.B.

Abstract

This paper deals with dynamic behaviors of Hopfield type neural network model of n(≥3) identical neurons with two time-delayed connections coupled in a star configuration. Delay dependent as well as independent local stability conditions about trivial equilibrium is found. Considering synaptic weight and time delay as parameters Hopf-bifurcation, steady-state bifurcation and equivariant steady state bifurcation criteria are given. The criterion for the global stability of the system is presented by constructing a suitable Lyapunov functional. Also conditions for absolute synchronization about the trivial equilibrium are also shown. Using normal form method and the center manifold theory the direction of the Hopf-bifurcation, stability and the properties of Hopf-bifurcating periodic solutions are determined. Numerical simulations are presented to verify the analytical results. The effect of synaptic weight and delay on different types of oscillations, e.g. in-phase, phase-locking, standing wave and oscillation death, has been shown numerically.

Suggested Citation

  • Kundu, Amitava & Das, Pritha & Roy, A.B., 2016. "Stability, bifurcations and synchronization in a delayed neural network model of n-identical neurons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 12-33.
    • Handle: RePEc:eee:matcom:v:121:y:2016:i:c:p:12-33
    DOI: 10.1016/j.matcom.2015.07.006
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    References listed on IDEAS

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    1. Yuan, Yuan, 2007. "Dynamics in a delayed-neural network," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 443-454.
    2. Tu, Fenghua & Liao, Xiaofeng & Zhang, Wei, 2006. "Delay-dependent asymptotic stability of a two-neuron system with different time delays," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 437-447.
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    Cited by:

    1. Pradeep, C. & Cao, Yang & Murugesu, R. & Rakkiyappan, R., 2019. "An event-triggered synchronization of semi-Markov jump neural networks with time-varying delays based on generalized free-weighting-matrix approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 41-56.
    2. Prants, Fabiola G. & Rech, Paulo C., 2017. "Complex dynamics of a three-dimensional continuous-time autonomous system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 132-139.

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