Heteroclinic chaotic behavior driven by a Brownian motion

In this paper we study the chaotic behavior of a planar ordinary differential system with a heteroclinic loop driven by a Brownian motion, an unbounded random forcing. Unlike the case of homoclinic loops, two random Melnikov functions are needed in order to investigate the intersection of stable segments of one saddle and unstable segments of the other saddle. We prove that for almost all paths of the Brownian motion the forced system admits a topological horseshoe of infinitely many branches. We apply this result to the Josephson junction and the soft spring Duffing oscillator.