Analytical modeling of distributions with invariant measure in Volterra stochastic systems

For nonlinear Volterra stochastic systems (VStS) with additive and parametric white noises (not obligatory Gaussian), exact and approximate methods for analytical modeling are considered. Analogies between mechanical and biological stochastic systems are discussed. Stability of stationary regular and irregular regimes in probabilistic first and second moments is studied. Special attention is paid to analytical modeling and stability analysis of stochastic processes in two-dimensional differential VStS. Some generalizations are considered.