Bifurcation Analysis of a Stochastically Driven Limit Cycle

We establish the existence of a bifurcation from an attractive random equilibrium to shear-induced chaos for a stochastically driven limit cycle, indicated by a change of sign of the first Lyapunov exponent. This relates to an open problem posed by Lin and Young (Nonlinearity 21:899-922, 2008) and Young (Nonlinearity 21:245-252, 2008), extending results by Wang and Young (Commun Math Phys 240(3):509-529, 2003) on periodically kicked limit cycles to the stochastic context.