Regime Switching in Coupled Nonlinear Systems: Sources, Prediction, and Control-Minireview and Perspective on the Focus Issue

Abstract

Regime switching, the process where complex systems undergo transitions between qualitatively different dynamical states due to changes in their conditions, is a widespread phenomenon, from climate and ocean circulation, to ecosystems, power grids, and the brain. Capturing the mechanisms that give rise to isolated or sequential switching dynamics, as well as developing generic and robust methods for forecasting, detecting, and controlling them is essential for maintaining optimal performance and preventing dysfunctions or even collapses in complex systems. This Focus Issue provides new insights into regime switching, covering the recent advances in theoretical analysis harnessing the reduction approaches, as well as data-driven detection methods and non-feedback control strategies. Some of the key challenges addressed include the development of reduction techniques for coupled stochastic and adaptive systems, the influence of multiple timescale dynamics on chaotic structures and cyclic patterns in forced systems, and the role of chaotic saddles and heteroclinic cycles in pattern switching in coupled oscillators. The contributions further highlight deep learning applications for predicting power grid failures, the use of blinking networks to enhance synchronization, creating adaptive strategies to control epidemic spreading, and non-feedback control strategies to suppress epileptic seizures. These developments are intended to catalyze further dialog between the different branches of complexity.