A review on methods for localization of hidden attractors

Numerous studies on nonlinear dynamical systems reveal the existence of hidden attractors and their connection with multi-stability and complex dynamical behaviors. The basin of a hidden attractor does not intersect with the neighborhood of any fixed point (if any) in the system. This makes the detection of hidden attractors obscure since easily obtained properties of fixed point do not lead to the basins of hidden attractors. Therefore, finding new methods for localizing hidden attractors is a major issue in global dynamical analysis. In this review, we firstly sum up the basic properties of hidden attractors and examine why identification and localization of hidden attractor is hard. Then, we list the various methods for localization of hidden attractors from the pioneer work in the field: numerical continuation method, perpetual point method, critical velocity surface method, and connecting curve method. The pros and cons of these methods are analyzed in the review. Finally, the current problems in the topic are addressed to provide guidelines for future study.