Emerging dynamic regimes and tipping points from finite empirical principles

Abstract

AbstractAll dynamical systems are transient. The dynamics of our world at biogeochemical, ecological, and astronomical scales exist in a transient state because our planet, Sun, and universe are evolving toward thermodynamic equilibrium. However, predicting the tipping points associated with major dynamical shifts in these systems remains a significant challenge. Here, we introduce a new theoretical framework to predict tipping points. Our approach builds on two empirical principles: Observations occur over a finite time, and changes are perceptible when system variations are substantial relative to reference values. As a consequence, processes governing the dynamics of a system can become inactive over an observation time, and tipping points are reached when the processes switch off or on. The two principles were encoded mathematically, defining dynamic weights: contributions relative to reference values of the dynamic processes to the rate-of-change of agents in the system for a finite observational time. Operationally, processes were considered active if their weights were above a critical threshold. Tipping points were defined as reaching critical thresholds that activated or inactivated processes. This Finite Observational Dynamics Analysis Method (FODAM) method predicted that a system with n underlying dynamic processes could display 2n different dynamic regimes. However, the regimes depend on the observational time. The tipping points predicted the conditions for regime shifts and also the resilience of quasi-stable systems to perturbations. The application of FODAM was illustrated with a Lotka-Volterra predator-prey model featuring the interaction of bacteria and bacteriophage. A Colab notebook was also developed and deployed online to facilitate the application of the method to other systems. We conclude the article by discussing how our new approach bridges prior frameworks describing tipping point dynamics and critical transitions. We also outline the application of the method to empirical data to predict tipping points in complex systems.