Tipping points in complex systems: from prediction to mitigation

Abstract

Many complex systems ranging from ecosystems to molecular systems are often at risk of an unexpected collapse or tipping to alternative states. Specifically, a tiny perturbation in an input condition resulting in large, sudden, and often irreversible changes in the state of a dynamical system is known as "tipping" or "critical transition". Well-known examples of tipping include the melting of Antarctic ice sheets (climate), the collapse of ecosystems (ecology), a crash of markets in finance (finance), transitions between cellular phenotypes (systems biology). Each of these sudden transitions has undesired consequences for natural systems and human well-beings. Hence, understanding critical transitions and their early predictions are crucial to managing catastrophes. This thesis investigates bifurcation-induced and rate-induced tippings with associated early warning signals (EWSs) for various biological systems. First, we investigate the impact of a dynamic environment on a coupled consumerresource model. We identify that the system has complex dynamics such as multistability and critical transitions. In a multistable region, we find the probability of attaining each alternative state employing basin stability. In addition, critical transitions are identified at different magnitudes in the presence of stochastic fluctuations. We also explore the efficacy of EWSs to forewarn critical transitions in the model. Next, in a socialecological two-species model, we analyze the effect of demographic and environmental noise. To study the effect of demographic noise, we identify all the birth-death processes corresponding to the model and derive the associated master equation. Moreover, the resilience of alternative steady states has been analyzed using probabilistic potential and mean first-passage time. Incorporating conservationist social norms helps the system to mitigate tipping despite higher harvesting rates. Further, in an ecosystem model with slow-fast timescales, we identify rate-induced transitions and calculate the critical rate of change using the geometric singular perturbation theory. In disease biology, Epithelial-hybrid-mesenchymal transitions are hallmarks of cancer metastasis, drug resistance, and tumor relapse. We show that EWSs can detect sudden transitions among epithelial, hybrid-E/M, and mesenchymal phenotypes. Our analysis reveals the unexpectedly large basin of attraction for a hybrid-E/M phenotype. We identify mechanisms that can potentially evade the transition to a hybrid-E/M phenotype. Finally, we evaluate the effect of intrinsic noise on driving tipping in a model of tumor metabolism. By defining a dominance game, we consider payoff-based reaction rates to incorporate intrinsic noise on the temporal evolution of tumor states. We find that the metabolic exploration rate can drive critical transitions from a high glycolysis frequency state to a low glycolysis frequency state. The EWSs analysis reveals the role of time series length on a successful prediction. Together, this thesis investigates sudden transitions, their prediction, and mitigation in diverse stochastic complex systems.