Global existence of periodic solutions in a six-neuron BAM neural network model with discrete delays

Authors:
Changjin Xu;Xiaofei He;Peiluan Li
Affiliations:
Guizhou Key Laboratory of Economics System Simulation, Guizhou College of Finance and Economics, Guiyang 550004, PR China;Zhangjiajie College of Jishou University, Zhangjiajie 427000, PR China;Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, PR China
Venue:
Neurocomputing
Year:
2011

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Abstract

In this paper, a six-neuron BAM neural network model with discrete delays is considered. Using the global Hopf bifurcation theorem for FDE due to Wu [Symmetric functional differential equations and neural networks with memory, Trans. Am. Math. Soc. 350 (1998) 4799-4838] and the Bendixson's criterion for high-dimensional ODE due to Li and Muldowney [On Bendixson' criterion, J. Differential Equations 106 (1994) 27-39], a set of sufficient conditions for the system to have multiple periodic solutions are derived when the sum of delays is sufficiently large.