THE NATURE OF BURSTING NOISES, STOCHASTIC RESONANCE AND DETERMINISTICCHAOS IN EXCITABLE NEURONS

We study the Hindmarsh-Rose model of excitable neurons and show that i n the asymptotic limit this monostable model can possess some kind of dynamical bistability: small-amplitude quasiharmonic and large-amplitu de relaxational oscillations can be simultaneously excited and their f ormation 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 ef fects take place even for such model parameters when hysteresis transf orms into a step and they disappear when this step is smoothed out eno ugh. We analyze some characteristics and conditions of formation of th e deterministic chaos. We emphasize that such dynamical bistability an d the effects related to it are universal phenomena and occur in a wid e class of dynamical systems of different nature including brusselator . (C) 1998 Elsevier Science B.V.