Stabilization of dynamical systems by adding a colored noise

Stabilization of dynamics of a system has been of great concern to research ers and practitioners over the years. It is observed that the system is mor e 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 beh avior is examined. It is then observed that, one can stabilize or destabliz e a large class of systems of ordinary differential equations (ODEs) and st ochastic differential equations (SDEs) if a noise is carefully added.