Modeling the Co-evolution of Climate Impact and Population Behavior: A Mean-Field Analysis

Motivated by the climate crisis currently ravaging the planet, we propose and analyze a novel framework for the coupled evolution of anthropogenic climate impact and human environmental behavior. Our framework includes a human decision-making process that captures social influence, government policy interventions, and the cost of acting environmentally friendly, modeled within a game-theoretic paradigm. By taking a mean-field approach at the limit of large populations, we derive the equilibria and their local stability characteristics. Subsequently, we study global convergence, showing that the system converges to a periodic solution for almost all initial conditions. Numerical simulations confirm our findings and suggest that the level of environmental impact might become dangerously high before the system reaches the periodic solution, calling for the design of optimal control strategies to influence the system trajectory.