Control of multistate hopping intermittency

In multistable regimes, noise can create multistate hopping intermittency, i.e., intermittent transitions among coexisting stable attractors. We demonstrate that a small periodic perturbation can significantly control such hopping intermittency. By control we imply a qualitative change in the probability distribution of occupation in the phase space around the stable attractors. In other words, if the uncontrolled system exhibits a preference to stay around a given attractor (say A) in comparison to another attractor (say B), the control perturbation creates a contrasting scenario so that attractor B is most frequently visited and consequently, the occupation probability becomes maximum around B instead of A. The control perturbation works in the following way: It destroys attractor A by boundary crisis while attractor B remains stable. As a result, even if the system is pushed by noise into the erstwhile basin of attractor A, the system does not remain there for long and therefore stays longer around attractor B. Significantly, such a change in the intermittent scenario can be obtained by a small-amplitude and slow-periodic perturbation. The control is theoretically demonstrated with two standard models, namely, Lorenz equations (for autonomous systems), and the periodically driven, damped Toda oscillator (for nonautonomous systems). Recent experiments with a cavity-loss modulated CO2 laser and an analog circuit of Lorenz equations have validated our theoretical demonstrations excellently.