Stability and bifurcation analysis on a discrete-time neural network

Authors:
Zhaohui Yuan;Dewen Hu;Lihong Huang
Affiliations:
College of Mechatronics and Automation, National University of Defense Technology, Changsha, Hunan 410073, PR China and College of Mathematics and Econometrics, Applied Mathematics, Hunan Universi ...;College of Mechatronics and Automation, National University of Defense Technology, Changsha, Hunan 410073, PR China;College of Mathematics and Econometrics, Applied Mathematics, Hunan University Changsha, Hunan 410082, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

Using techniques developed by Kuznetsov to discrete-time systems, we study the stability of the equilibrium (0, 0) and Neimark-Sacker bifurcation (also called Hopf bifurcation for map) of a discrete-time neural network system. The obtained results are less restrictive and improve upon the existing ones on Neimark-Sacker bifurcation of discrete-time neural network with special classes of transfer functions. The theoretical analyses are verified by numerical simulations. Our results have potential applications in neural networks.