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A first approximation of the quasipotential in problems of the stability of systems with random non-degenerate perturbations

Authors
Journal
Journal of Applied Mathematics and Mechanics
0021-8928
Publisher
Elsevier
Publication Date
Volume
59
Issue
1
Identifiers
DOI: 10.1016/0021-8928(95)00006-b
Disciplines
  • Mathematics

Abstract

Abstract The problem of a local description (near to a stationary point or orbit) of the quasipotential—the Lyapunov function, used when analysing the stability of a system with small non-degenerate random perturbations is considered. First approximations are constructed for quasipotentials in neighbourhoods of these invariant sets. The quadratic forms specifying these approximations are goverened by certain matrices. The construction of these matrices is reduced to the solution of Lyapunov matrix equations (which are algebraic in the case of stationary points, and differential with periodic coefficients in the case of orbits).

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