Transition to chaos in continuous-time random dynamical systems

A continuous-time dynamical system in which a nonchaotic attractor coexists with a nonattracting chaotic saddle, was discussed. The fundamental dynamical mechanism responsible for the transition was investigated. A general scaling low for the largest Lyapunov exponent, was obtained. The topology of the flow was fundamentally disturbed after the onset of noisy chaos. It was found that such a disturbance was due to changes in the number of unstable eigendirections along a continuous trajectory under the influence of noise.