Commenced in January 2007
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Global Existence of Periodic Solutions in a Delayed Tri–neuron Network

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

In this paper, a tri–neuron network model with time delay is investigated. By using the Bendixson-s criterion for high– dimensional ordinary differential equations and global Hopf bifurcation theory for functional differential equations, sufficient conditions for existence of periodic solutions when the time delay is sufficiently large are established.

Keywords: Delay, global Hopf bifurcation, neural network, periodicsolutions.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1055170

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[1] Xiaoming Liu, Xiaofeng Liao. Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay. Chaos, Solitons and Fractals, 40(2009), 481-490.
[2] P D Gupta, N C Majee, A B Roy. Stability, bifurcation and global existence of a Hopf-bifurcating periodic solution for a class of three- neuron delayed network models. Nonlinear Analysis, 67(2007), 2934- 2954.
[3] Bingji Xu, Xinzhi Liu, Xiaoxin Liao. Global asymptotic stability of high- order Hopfield type neural networks with time delays. Computers and Mathematics with Applications, 45(2003), 1729-1737.
[4] Qiang Zhang, Xiaopeng Wei, Jin Xu. Global asymptotic stability of Hopfield neural networks with transmission delays. Physics Letters A, 318(2003), 399-405.
[5] Bingwen Liu, Lihong Huang. Existence and exponential stability of periodic solutions for cellular neural networks with time-varying delays. Physics Letters A, 349(2006), 474-483.
[6] Bingwen Liu, Lihong Huang. Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays. Physics Letters A, 341(2006), 135-144.
[7] Chunrui Zhang, Baodong Zheng. Hopf bifurcation in numerical approximation of a n−dimension neural network model with multi-delays. Chaos, Solitons and Fractals, 25(2005), 129-146.
[8] M Y Li, J Muldowney. On Bendixson-s criterion. Journal of Differential Equations, 106(1993), 27-39.
[9] Jianhong Wu. Symmetric functional differential equations and neural networks with memory. Transactions of the AMS, 350(1998), 4799-4838.