Critical transitions and intelligent control in complex systems

Abstract Critical transitions, or ‘tipping points’, are abundant across physical, engineering and biological systems. These infrequent but substantial occurrences—resembling ‘black swan’ events—can trigger abrupt and irreversible changes in neurological health, climate dynamics and ecosystem resilience. Surpassing a critical threshold often represents a point of no return, making the detection and prediction of these phenomena essential for mitigating their far-reaching consequences. By integrating stochastic and nonlinear dynamical systems, topological methods, non-equilibrium statistical mechanics and machine learning with observational data, a natural framework emerges for modelling, simulating and predicting these transitions. This thematic issue presents 12 articles that advance our understanding of tipping mechanisms, early warning indicators and intelligent control strategies. This article is part of the theme issue ‘Critical transitions and intelligent control in complex systems’.