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

Amitava Kundu, Pritha Das and A.B. Roy

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 121, issue C, 12-33

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.

Keywords: Multiple-delay; Local stability; Global stability; Bifurcation; Synchronization (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:121:y:2016:i:c:p:12-33

DOI: 10.1016/j.matcom.2015.07.006

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