Title: Complex dynamics and stability of Hopfield neural networks with delays

Authors: S.J. Guo, J.B. Guan, Xinchu Fu

Addresses: Department of Mathematics, Shanghai University, Shanghai 200444, PR China; School of Physics and Mathematics, Jiangsu Polytechnic University, Changzhou 213164, PR China. ' Department of Mathematics, Shanghai University, Shanghai 200444, PR China. ' Department of Mathematics, Shanghai University, Shanghai 200444, PR China

Abstract: In this paper, by utilising the Lyapunov functional method, we analyse the global asymptotic stability of Hopfield neural networks with delays. We obtain some new sufficient conditions to ensure the global asymptotic stability of the model being independent of delays. By using the Lyapunov second method for special cases, we also get that the equilibrium of the system is locally asymptotically stable when the delay is under a critical value; and when the delay is equal to this value, Hopf bifurcation will occur and the equilibrium is unstable; and when the delay is above the critical value, the system will demonstrate complex dynamics. Finally, numerical simulations are presented to verify the analytical results.

Keywords: equilibrium; delays; global asymptotical stability; Hopf bifurcation; complex dynamics; Hopfield neural networks.

DOI: 10.1504/IJSCC.2009.026321

International Journal of Systems, Control and Communications, 2009 Vol.1 No.4, pp.437 - 452

Published online: 06 Jun 2009 *

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