Modeling Stochastic resonance and its manifestation in brain cells

Author: Sophie Abramishvili
Keywords: Modeling, bistable system, signal amplification, brain cells
Annotation:

Stochastic resonance is an interesting phenomenon, in which, the effect of a weak, periodic force, is amplified with a chaotic force. It is involved in many processes: in the hearing apparatus of the crab, in the amplification of the wave signal, and according to the latest researches, probably in the brain cells as well. We consider a bistable Duffing oscillator, with 3 different types of forces acting on it: sinusoidal, square and triangular (separately). The amplitude of the forces is not sufficient to move the system from one state to another, so we add a chaotic force to the system which has a white noise distribution, and by selecting the required parameters we obtain a stochastic resonance, during which the system starts oscillating with a chaotic force with the frequency of a weak periodic force. The model is assembled and solved numerically in Mathlab: a second order differential equation is constructed and the Runge-Kutta scheme is used to solve it.