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.