Stability switches and bifurcation analysis of a neural network with continuously delay

Authors:
Xiaofeng Liao;Zhongfu Wu;Juebang Yu
Affiliations:
Dept. of Opto-Electron. Technol., Univ. of Electr. Sci. & Technol. of China, Sichuan;-;-
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Year:
1999

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Abstract

A continuously delayed neural network with strong kernel is investigated. We found that a switch from stability to instability may occur for certain range of system parameters and must then be followed by a switch back to stability. We also investigate bifurcation phenomena of this model. Using the mean time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs, i.e., a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter passes through a critical value. Stability criteria for the bifurcating periodic solutions are obtained. Some computer simulations illustrate correctness of the results