Controlling monostability in a bistable system

The majority of nonlinear systems are characterized by coexistence of two or more dynamical equilibrium states for the same set of parameters. For example, in optical devices some kinds of instabilities result from the coexistence of multiple attractors and occasional involuntary jump of the system from one attractor to another. Thus, the stabilization of dynamical system is often related to the problem of controlling monostability. We propose a unique method, which allows one to eliminate one of the coexisting states, so that the system becomes monostable. The method implies a slow periodic modulation of a system parameter. We develop this method on the basis of a loss-driven CO₂ laser