Control of multistate hopping intermittency

Abstract

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.