Stabilization of dynamical systems by adding a colored noise

Stabilization of dynamics of a system has been of great concern to researchers and practitioners over the years. It is observed that the system is more viscous if one adds a noise in the system. In the present situation, the system is perturbed by a (multiplicative) noise and the stable/unstable behavior is examined. It is then observed that, one can stabilize or destablize a large class of systems of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) if a noise is carefully added.