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Multiple Hopf bifurcations of symmetric BAM neural network model with delay. (English) Zbl 1178.34105
The paper investigates a symmetric BAM neural network model with delay. By analyzing the corresponding characteristic equations, the authors first consider the existence of Hopf bifurcations. The existence of multiple periodic solutions is established using a symmetric Hopf bifurcation result developed by J. Wu [“Symmetric functional-differential equations and neural networks with memory”, Trans. Am. Math. Soc. 350, No. 12, 4799–4838 (1998; Zbl 0905.34034)].
MSC:
34K60Qualitative investigation and simulation of models
34K18Bifurcation theory of functional differential equations
34K13Periodic solutions of functional differential equations
92B20General theory of neural networks (mathematical biology)
References:
[1]Kosto, B.: Bidirectional associative memories, IEEE transactions on system man and cybernetics 18, 49-60 (1988)
[2]Gopalsamy, K.; He, X.: Delay-independent stability in bi-directional associative memory networks, IEEE transactions on neural network 5, 998-1002 (1994)
[3]Huang, X.; Cao, J.: LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks, Chaos, solitons and fractals 24, No. 3, 885-898 (2005) · Zbl 1071.82538 · doi:10.1016/j.chaos.2004.09.037
[4]Guo, S.; Huang, L.; Dai, B.; Zhang, Z.: Global existence of periodic solutions of BAM neural networks with variable coefficients, Physics letters A 317, 97-106 (2003) · Zbl 1046.68090 · doi:10.1016/j.physleta.2003.08.019
[5]Park, Ju H.: A novel criterion for global asymptotic stability of BAM neural networks with time delays, Chaos, solitons and fractals 29, No. 2, 446-453 (2006) · Zbl 1121.92006 · doi:10.1016/j.chaos.2005.08.018
[6]Yuan, Y.: Dynamics in a delayed-neural network, Chaos, solitons and fractals 33, No. 2, 443-454 (2007) · Zbl 1135.34039 · doi:10.1016/j.chaos.2006.01.018
[7]Yuri, A. K.: Elements of applied bifurcation theory, (1995)
[8]Dias, Ana Paula S.; Lamb, Jeroen S. W.: Local bifurcation in symmetric coupled cell networks: linear theory, Physica D 223, No. 1, 93-108 (2006) · Zbl 1112.34025 · doi:10.1016/j.physd.2006.08.014
[9]Wu, J.: Symmetric functional differential equations and neural networks with memory, Transactions of the American mathematical society 350, No. 12, 4799-4838 (1998) · Zbl 0905.34034 · doi:10.1090/S0002-9947-98-02083-2