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Motivated by the climate crisis that is currently ravaging the planet, wepropose and analyze a novel framework for the evolution of anthropogenicclimate impact in which the evolution of human environmental behavior andenvironmental impact is coupled. Our framework includes a human decision-makingprocess that captures social influence, government policy interventions, andthe cost of environmentally-friendly behavior, modeled within a game-theoreticparadigm. By taking a mean-field approach in the limit of large populations, wederive the equilibria and their local stability characteristics. Subsequently,we study global convergence, whereby we show that the system converges to aperiodic solution for almost all initial conditions. Numerical simulationsconfirm our findings and suggest that, before the system reaches such aperiodic solution, the level of environmental impact might become dangerouslyhigh, calling for the design of optimal control strategies to influence thesystem trajectory.

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