Bifurcations in Stochastic Systems—A Generalized Hermite Analysis

by Walter V. Wedig, Univ of Karlsruhe, Germany,

Abstract: Ito calculus and Markov theory are powerful tools to investigate nonlinear dynamic systems. Consequently, we need an extended experience to solve Fokker-Planck equations. In a more recent approach generalized Hermite polynomials are introduced to calculate eigenvalues and eigenvectors of parabolic operators. Applications are discussed for nonlinear dynamic systems with parameter fluctuations or external excitations.

Subject Headings: Nonlinear response | Nonlinear analysis | Paraboloid | Dynamic analysis | Markov process | Polynomials | Eigenvalues

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