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 addresses an open problem posed by Kevin Lin and Lai-Sang Young, extending results by Qiudong Wang and Lai-Sang Young on periodically kicked limit cycles to the stochastic context.