Predicting noise-induced critical transitions in bistable systems

Critical transitions from one dynamical state to another contrasting state are observed in many complex systems. To understand the effects of stochastic events on critical transitions and to predict their occurrence as a control parameter varies are of utmost importance in various applications. In this paper, we carry out a prediction of noise-induced critical transitions using a bistable model as a prototype class of real systems. We find that the largest Lyapunov exponent and the Shannon entropy can act as general early warning indicators to predict noise-induced critical transitions, even for an earlier transition due to strong fluctuations. Furthermore, the concept of the parameter dependent basin of the unsafe regime is introduced via incorporating a suitable probabilistic notion. We find that this is an efficient tool to approximately quantify the range of the control parameter where noise-induced critical transitions may occur. Our method may serve as a paradigm to understand and predict noise-induced critical transitions in multistable systems or complex networks and even may be extended to a broad range of disciplines to address the issues of resilience.