Controlling the multistability of nonlinear systems with coexisting attractors

A method for controlling generalized multistability is suggested. The method implies the application of a small harmonic modulation with properly chosen frequency and amplitude to a system parameter. The possibility of control is demonstrated with the example of the Hénon map with coexisting period-1, period-3, and period-9 attractors. It is shown that one or more coexisting attractors can lose their stability and the attractor can undergo crisis when the control frequency is close to the relaxation oscillation frequency or its subharmonics of the corresponding attractor.