The nature of bursting noises,stochastic resonance and deterministic chaos in excitable neurons |
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| Affiliation: | 1. Department of Applied Mechanics, IIT Madras, Chennai 600 036, India;2. Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus-741246, West Bengal, India;1. Department for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India;2. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, India;3. Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India;4. Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China;1. Imec, Kapeldreef 75, B-3001 Leuven, Belgium;2. Instituut voor Kern- en Stralingsfysica, K. U. Leuven, B-3001 Leuven, Belgium |
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| Abstract: | We study the Hindmarsh-Rose model of excitable neurons and show that in the asymptotic limit this monostable model can possess some kind of dynamical bistability: small-amplitude quasiharmonic and large-amplitude relaxational oscillations can be simultaneously excited and their formation is accompanied by a narrow hysteresis. We show that bursting noises, stochastic resonance and deterministic chaos are determined by random transitions between these two dynamical states under slow and small changes of one of the model variables (z). We find that these effects take place even for such model parameters when hysteresis transforms into a step and they disappear when this step is smoothed out enough. We analyze some characteristics and conditions of formation of the deterministic chaos. We emphasize that such dynamical bistability and the effects related to it are universal phenomena and occur in a wide class of dynamical systems of different nature including brusselator. |
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