Abstract
Complex dynamical behavior in a four-neuron recurrent neural network with discrete delays is investigated in this paper. The dissipativity of the system and stability of equilibrium point are studied by mens of Lyapunov theory. Stable fixed point, periodic and quasi-periodic orbits, and chaotic motion are observed in system via numerical calculation. With the change of the slope and threshold of activation function, as well as time delay and synaptic weight, the system passes from stable to periodic and then to chaotic regimes. Interestingly, the system returns to periodic or stable regimes by further changing these parameter values. Furthermore, some numerical evidences, such as phase portraits, bifurcation diagrams, power spectrum density, are given to confirm chaos.
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References
Shen, Y., Zhao, G.Y., Jiang, M.H., Mao, X.R.: Stochastic Lotka-Volterra Competitive Systems with Variable Delay. In: Huang, D.-S., Zhang, X.-P., Huang, G.-B. (eds.) ICIC 2005. LNCS, vol. 3645, pp. 238–247. Springer, Heidelberg (2005)
Zeng, Z.G., Wang, J., Liao, X.X.: Stability Analysis of Delayed Cellular Neural Networks Described Using Cloning Templates. IEEE Trans. Circuits and Systems I 51, 2313–2324 (2004)
Zeng, Z.G., Huang, D.S., Wang, Z.F.: Global Stability of A General Class of Discrete-time Recurrent Neural Networks. Neural Processing Letters 22, 33–47 (2005)
Shen, Y., Zhao, G.Y., Jiang, M.H., Hu, S.G.: Stochastic High-order Hopfield Neural Networks. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3610, pp. 740–749. Springer, Heidelberg (2005)
Shen, Y., Jiang, M.H., Liao, X.X.: Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-varying Delays and Continuously Distributed Delays. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 156–161. Springer, Heidelberg (2005)
Das, A., das, P., Roy, A.B.: Chaos in Three Dimensional Neural Network. Applied Mathematical Modelling 24, 511–522 (2000)
Das, A., das, P., Roy, A.B.: Chaos in A Three-dimensional Model of Neural Network. Int. J. of Bifur. and Chaos 12, 2271–2281 (2002)
Li, C.G., Yu, J.B., Liao, X.F.: Chaos in A Three-neuron Hysteresis Hopfield-type Neural Network. Physics Letters A 285, 368–372 (2001)
Liao, X.F., Wong, K.W., Leung, C.S., Wu, Z.F.: Hopf Bifurcation and Chaos in A Single Delayed Neuron Equation with Non-monotonic Activation Function. Chaos, Solitons and Fractals 12, 1535–1547 (2001)
Zhou, S.B., Liao, X.F., Yu, J.B., Wong, K.W.: Chaos and Its Synchronization in Two-neuron Systems with Discrete Delays. Chaos, Solitons and Fractals 21, 133–142 (2004)
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Luo, H., Xu, X., Liao, X. (2006). Numerical Analysis of a Chaotic Delay Recurrent Neural Network with Four Neurons. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_51
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DOI: https://doi.org/10.1007/11759966_51
Publisher Name: Springer, Berlin, Heidelberg
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