Deep Learning and Dynamical Systems Approaches to Critical Transitions in Socio–Climate and Complex Systems

Abstract

This thesis explores how dynamical systems, stochastic processes, and deep learning can be integrated to study critical transitions in socio-climate and other complex systems. Chapter 1 establishes the conceptual foundation, introducing complex systems, tipping points, bifurcation theory, stochasticity, early warning signals, and the role of deep learning. It also highlights flickering as a precursor to collapse and motivates the importance of coupled socio-climate feedbacks. Chapter 2 develops a hybrid CNN--LSTM framework to classify bifurcations in noisy time series. Trained on synthetic dynamical models, the classifier generalises to empirical data and outperforms traditional early warning signals, offering a robust method to identify fold, Hopf, and transcritical bifurcations. Chapter 3 introduces a deep learning approach to detect flickering dynamics, noise-driven switching between alternative equilibria. The model distinguishes true flickering from noise-induced variance inflation across diverse systems and demonstrates applicability to empirical data such as palaeoclimate records and physiological signals, providing an early warning beyond variance-based methods. Chapter 4 presents a coupled socio-climate model where social behaviour feeds back on emissions and climate thresholds. Results show that social dynamics, such as faster learning rates or stronger norms, can delay or prevent climate tipping, while delays or weak norms accelerate collapse. This chapter highlights the potential of social tipping points to stabilize climate trajectories. Chapter 5 evaluates whether binary opinion models suffice to represent socio-climate interactions compared to richer spectrum models. Using replicator and Friedkin–Johnsen frameworks coupled to climate-carbon and forest-grassland systems, the study finds that binary models capture essential coupled dynamics with surprising accuracy, despite their simplicity. Together, the chapters demonstrate that combining dynamical systems theory, stochastic analysis, and deep learning yields powerful tools to anticipate tipping points. The findings advance both methodological development and practical insight, showing that human social responses can critically shape whether climate transitions are mitigated or exacerbated.