Abstract
In nonlinear dynamical systems, noise can lead to qualitative changes in their behaviors, not quantitative changes. We study the effects of noise on the nonlinear chaotic neuron in the state having chaos. We show that noise induces the systems producing more order and the coherence of their noise-induced order becomes maximal for a certain noise amplitude. This effect is indicated to be a transition from chaotic behavior to ordered(non-chaotic) behavior by evaluating the Lyapunov exponent with noise.
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References
Gammaitoni, L., Hänggi, P., Jung, P., Marchesoni, F.: Stochastic Resonance. Rev. Mod. Phys. 70, 223–287 (1998)
Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Science. Cambridge University Press, Cambridge (2001)
Anishchenko, V.S., Astakhov, V.V., Neiman, A.B., Vadivasova, T.E., Schimansky-Geier, L.: Nonlinear Dynamics of Chaotic and Stochastic System. Springer, Heidelberg (2002)
Matsumoto, K., Tsuda, I.: Noise-induced order. J. Stat. Phys. 31, 87–106 (1983)
Crutchfield, J.P., Farmer, J.D., Huberman, B.A.: Fluctuations and Simple Chaotic Dynamics. Phys. Rep. 92, 46–82 (1982)
Kaneko, K., Tsuda, I.: Complex Systems: Chaos and Beyond - A Constructive Approach with Applications in Life Sciences. Springer, Heidelberg (2000)
Pikovsky, A.S., Kurths, J.: Coherence Resonance in a Noise-Driven Excitable System. Physical Review Letters 78, 775–778 (1997)
Freeman, W.J.: Neurodynamics: an exploration in mesoscopic brain dynamics. Springer, Heidelberg (2000)
Arbib, M.A. (ed.): The Handbook of Brain Theory and Neural Networks, 2nd edn. Bradford Books (2002)
Korn, H., Faure, P.: Is there chaos in the brain? II. experimental evidence and related models. C.R. Biologies 326, 787–840 (2003)
Takabe, T., Aihara, K., Matsumoto, G.: Response characteristics of the Hodgkin-Huxley equations to pulse-train stimulation. IEICE Trans. Commun. (A), J71-A(3), 744–750 (1988) (in Japanese)
Aihara, K.: Chaotic Neural Networks. In: Kawakami, H. (ed.) Bifurcation Phenomena in Nonlinear Systems and Theory of Dynamical Systems, pp. 143–161. World Scientific, Singapore (1990)
Aihara, K., Takabe, T., Toyoda, M.: Chaotic Neural Networks. Physics Letters A 144, 333–340 (1990)
Nishimura, H., Aihara, K.: Coaction of neural networks and chaos. Journal of The Society of Instrument and Control Engineers 39(3), 162–168 (2000) (in Japanese)
Parker, T.S., Chua, L.O.: Practical Numerical Algorithms for Chaotic Systems. Springer, Heidelberg (1989)
Paladin, G., Serva, M., Vuipiani, A.: Complexity in Dynamical Systems with Noise. Physical Review Letters 74, 66–69 (1995)
Witt, A., Neiman, A., Kurths, J.: Characterizing the Dynamics of Stochastic Bistable Systems by Measures of Complexity. Phys. Rev. E55, 5050–5059 (1997)
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Katada, N., Nishimura, H. (2010). Noise Effects on Chaos in Chaotic Neuron Model. In: Peper, F., Umeo, H., Matsui, N., Isokawa, T. (eds) Natural Computing. Proceedings in Information and Communications Technology, vol 2. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53868-4_24
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DOI: https://doi.org/10.1007/978-4-431-53868-4_24
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