Finding coexisting attractors using amplitude control

Nonlinear dynamical systems often have multiple stable states and thus can harbor coexisting and hidden attractors that may pose an inconvenience or even hazard in practical applications. Amplitude control provides one method to detect these coexisting attractors, and it explains the unpredictable and irreproducible behavior that sometimes occurs in carefully engineered systems. In this paper, two regimes of amplitude control are described to illustrate the method for detecting multistability and possible coexisting or hidden attractors.