On vibrational stabilization of nonlinear dynamic systems (Q1088964)

The stabilization of the stationary state of a nonlinear system is considered with the aid of periodic variations of its parameters. Sufficient conditions are presented for the existence of an asymptotically stable periodic solution in a small neighborhood of the initial stationary state. Under these conditions the original problem reduces to a linear problem. A method of solution of the linear problem is presented, and also an example of vibrational stabilization of an unstable stationary mode of a continuous perfect-mixing chemical reactor.