Chaotic Behavior in Differential Equations Driven by a Brownian Motion
نویسندگان
چکیده
In this paper, we investigate the chaotic behavior of ordinary differential equations with a homoclinic orbit to a dissipative saddle point under an unbounded random forcing driven by a Brownian motion. We prove that, for almost all sample pathes of the Brownian motion in the classical Wiener space, the forced equation admits a topological horseshoe of infinitely many branches. This result is then applied to the randomly forced Duffing equation and the pendulum equation.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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