期刊
MATHEMATICS AND COMPUTERS IN SIMULATION
卷 121, 期 -, 页码 12-33出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.matcom.2015.07.006
关键词
Multiple-delay; Local stability; Global stability; Bifurcation; Synchronization
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. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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