Many nonlinear systems exhibit the coexistence of multiple dynamic equilibrium status in some regions of parameter space. This phenomenon, referred to as generalized multistability, is found in variety of systems from different fields, including electronics, optics, mechanics, and biology, in addition to some standard models like Hénon map, Duffing, Rössler, van del Pol, and Lorentz equations. In such multiattractor systems a final state depends crucially on the initial conditions. However, in many practical situations multistability can create inconvenience, for instance, in construction of a commercial device with determinate characteristics. Therefore, the control of multistability is an important problem in applied nonlinear science. A method for controlling multistability was suggested by Pisarchik and Goswami in 2000. The authors called up the idea of complete annihilation of undesirable attractors in order to make the system monostable. They shown that undesirable states can be destroyed by a weak periodic modulation applied to a system parameter. Later, the method has been used for controlling multistability in coupled Duffing oscillators, a time-delayed logistic map, and lasers. The method has been realized experimentally in a CO laser and an erbium-doped fiber laser.
In this report we demonstrate that the method of attractor annihilation also work in a noisy system. As an example, we explore the noisy Hénon map wich is described as