Bifurcation Analysis of a Stochastically Driven Limit Cycle

Abstract

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.

References in corpus (2)

• Shear-Induced Chaos
• Hopf bifurcation with additive noise

Cited by in corpus (8)

• A Random Dynamical Systems Perspective on Isochronicity for Stochastic Oscillations
• Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems
• Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise
• Transition to anomalous dynamics in a simple random map
• Lower bounds on the Lyapunov exponents of stochastic differential equations
• A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations
• A General View on Double Limits in Differential Equations
• The conditioned Lyapunov spectrum for random dynamical systems