The dynamical system response to a small change of the right-hand side and finite dimensional analogues of the Fokker-Planck equation. (Russian, English) Zbl 1074.82024

Noarov, A. I.

Zh. Vychisl. Mat. Mat. Fiz. 45, No. 7, 1237-1250 (2005); translation in Comput. Math. Math. Phys. 45, No. 7, 1195-1208 (2005).

Author’s summary: The change of a steady-state solution to the Fokker-Planck equation in response to small variations of the right-hand side (vector field) of the corresponding unperturbed system is investigated. Certain functionals of a steady-state solution and their dependence on the right-hand side of the unperturbed system are considered. This dependence is linearized, and an algorithm for computing its linear part is constructed. The applicability of the developed method to the control of dynamical systems is discussed.

Reviewer: Andrei Zemskov (Moskva)

MSC:

82C31	Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
65C30	Numerical solutions to stochastic differential and integral equations

Keywords:

Fokker-Planck equation; stochastic differential equation; chaotic dynamics