Stability of First Order Ordinary Differential Equations with Colored Noise Forcing
نویسندگان
چکیده
We present a method for determining the stability of a class of stochastically forced ordinary differential equations, where the forcing term can be obtained by passing white noise through a filter of arbitrarily high degree. We use the Fokker-Planck equation to write a partial differential equation for the second moments, which we turn into an eigenvalue problem for a second-order differential operator. The eigenvalues of this operator determine the stability of the system. Inspired by Dirac’s creation and annihilation operator method, we develop “ladder” operators to determine analytic expressions for the eigenvalues and eigenfunctions of our operator.
منابع مشابه
Stability of Ordinary Differential Equations with Colored Noise Forcing
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