Noise Effects on Chaos in Chaotic Neuron Model

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.

[1]  Walter J. Freeman,et al.  Neurodynamics: An Exploration in Mesoscopic Brain Dynamics , 2000, Perspectives in Neural Computing.

[2]  J. Kurths,et al.  Coherence Resonance in a Noise-Driven Excitable System , 1997 .

[3]  B. Huberman,et al.  Fluctuations and simple chaotic dynamics , 1982 .

[4]  Vulpiani,et al.  Complexity in dynamical systems with noise. , 1995, Physical review letters.

[5]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[6]  Ichiro Tsuda,et al.  Noise-induced order , 1983 .

[7]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[8]  Alexander B. Neiman,et al.  Characterizing the dynamics of stochastic bistable systems by measures of complexity , 1997 .

[9]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[10]  Alexander B. Neiman,et al.  Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments , 2003 .

[11]  K. Aihara,et al.  Chaotic neural networks , 1990 .

[12]  Kunihiko Kaneko,et al.  Complex Systems: Chaos and Beyond: A Constructive Approach with Applications in Life Sciences , 2000 .

[13]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[14]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[15]  Philippe Faure,et al.  Is there chaos in the brain? II. Experimental evidence and related models. , 2003, Comptes rendus biologies.