Abstract
In this paper, the chaos synchronization between two delayed neuron chaotic systems with linearly bi-directional coupling is investigated. Some generic criterion is developed for choosing the appropriate coupling parameters to ensure global chaos synchronization based on Krasovskii-Lyapunov theory. Finally, numerical results illustrate the effectiveness of the criterion.
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References
Gilli, M.: Strange Attractors in Delayed Cellular Neural Networks. IEEE Trans Circuits Syst 40, 849–853 (1993)
Liao, X.F., Wong, K.W., Wu, Z.F.: Bifurcation Analysis on a Two-neuron System with Distributed Delays. Physica D 149, 123–141 (2001)
Zou, J.A., Nossek: Bifurcation and Chaos in Cellular Neural Networks. IEEE Trans Circuits Syst. 40, 166–173 (1993)
Chen, L.N., Aihara, K.: Chaos and Asymptotical Stability in Discrete-time Neural Networks. Physica D 104, 286–325 (1997)
Das, A., Roy, A.B., Das, P.: Chaos in a Three Dimensional Neural Network. Applied Mathematical Modeling 24, 511–522 (2000)
Li, C.G., Yu, J.G., Liao, X.F.: Chaos in a Three-neuron Hysteresis Hopfield-type Neural Network. Physics Letters A 285, 368–372 (2001)
Dror, G., Tsodyks, M.: Chaos in Neural Networks with Dynamic Synapses. Neurocomputin 32-33, 365–370 (2000)
Liao, X.F., Li, S.W., Chen, G.R.: Bifurcation Analysis on a Two-neuron System with Distributed Delays in the Frequency Domain. Neural Networks 17, 545–561 (2004)
Hopfield, J.J.: Neurons with Graded Response Have Collective Computational Properties Like Those of Two-state neurons. Proc Natl. Acad. Sci. USA 81, 3088–3092 (1984)
Liao, X.F., Wong, K.W., Leung, C.S., Wu, Z.F.: Hopf Bifurcation and Chaos in a Single Delayed Neural Equation with Non-monotonic Activation Function. Chaos, Solitons & Fractals 12, 1535–1547 (1999)
Liao, X.F., Wong, K.W., Wu, Z.F.: Asymptotic Stability Criteria for a Two-neuron Network with Different Time Delays. IEEE Trans. NN 14, 222–227 (2003)
He, G.G., Cao, Z.T.: Controlling Chaos in a Chaotic Neural Network. Neural Networks 16, 1195–1200 (2003)
Aihara, K., Takabe, T., Toyoda, M.: Chaotic Neural Networks. Physical Letters A 144, 333–340 (1990)
Degn, H., Holden, A.V., Olsen, L.F. (eds.): Chaos in Biological Systems. Plenum Press, New York (1987)
Adachi, M.: Controlling a Simple Chaotic Neural Network Using Response to Perturbation. In: Proceedings of NOLTA 1995, pp. 989–992 (1995)
Adachi, M., Aihara, K.: Associative Dynamics in a Chaotic Neural Network. Neural Networks 10, 83–98 (1997)
Zhou, S.B., Liao, X.F.: Chaos and Its Synchronization in Two-neuron Systems with Discrete Delays. Chaos, Solitons and Fractals 21, 133–142 (2004)
Lu, W.L., Chen, T.P.: Synchronization of Coupled Connected Neural Networks With Delays. IEEE Trans. Circuits and Syst 51, 2491–2503 (2004)
Pyragas, K.: Synchronization of Coupled Time-delay Systems: Analytical Estimations. Phy. Rev. E 58, 3067–3071 (1998)
Pasemann, F.: Synchronized Chaos and Other Coherent States for Two Coupled Neurons. Physica D 128, 236–249 (1999)
Gopalsamy, K., Leung, K.: Convergence Under Dynamical Thresholds with Delays. IEEE Trans NN 8, 341–348 (1997)
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Zhang, X., Zhou, S. (2005). Chaos Synchronization for Bi-directional Coupled Two-Neuron Systems with Discrete Delays. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_55
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DOI: https://doi.org/10.1007/11427391_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25912-1
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