Suppression of noise-induced critical transitions: a linear augmentation method

Abstract

In stochastic complex systems, some sudden critical transitions (CTs) from one desirable state to another contrasting one can take place because of noise, which may even lead to catastrophic consequences. To keep a certain system in one desirable state of performance, methods that suppress these catastrophic CTs in the presence of noise need to be developed. In this paper, the ability of an external linear augmentation method to suppress Gaussian white noise-induced CTs away from a desirable state is investigated from a new perspective. This control is designed in such a way that, as a noise-induced CT is impending, the desirable state of performance in a stochastic complex system can be stabilized using a specific type of coupling with a linear dynamical system. Then, the contrasting state is annihilated with increasing coupling strength. Taking a bi-stable system with one CT (from the desirable state to the undesirable one) and a tri-stable system with two CTs (from the desirable state to the sub-desirable one and from the sub-desirable state to the undesirable one) as the prototype class of real complex systems, the potential of our technique is demonstrated.