Delay-Induced Hopf Bifurcation and Periodic Solution in a BAM Network with Two Delays

Authors:
Jian Xu;Kwok Wai Chung;Ju Hong Ge;Yu Huang
Affiliations:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, P.R. China 200092;Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong;School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, P.R. China 200092;School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, P.R. China 200092
Venue:
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
Year:
2009

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Abstract

The time delays in neural networks come from the transformation of the information processing between neurons. To consider delay-induced dynamics in neural networks, the four neurons are coupled to model a called bidirectional associative memory neural network. If the transformation time is distinct in the two direction, then two delays occurs in the model. a simple but efficient method is first introduced and then the delay-induced Hopf bifurcation is investigated and the periodic approximate solution derived from the Hopf bifurcation is obtained analytically. It can be seen that theoretical prediction is in good agreement with the result from the numerical simulation, which shows that the provided method is valid. The results show also that the method has higher accuracy than the center manifold reduction (CMR) with norm form theory.