Stochastical aspects of neuronal dynamics: Fokker-Planck approach

The stochastical aspects of noise-perturbed neuronal dynamics are studied via the Fokker-Planck equation by considering the Langevin-type relaxational, nonlinear process associated with neuronal states. On the basis of a canonical, stochastically driven, dichotomous state modeling, the equilibrium conditions in the neuronal assembly are analyzed. The markovian structure of the random occurrence of action potentials due to the disturbances (noise) in the neuronal state is considered, and the corresponding solutions relevant to the colored noise spectrum of the disturbance effects are addressed. Stochastical instability (Lyapunov) considerations in solving discrete optimization problems via neural networks are discussed. The bounded estimate(s) of the stochastical variates involved are presented, and the noise-induced perturbations on the saturated-state neuronal population are elucidated.