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

TL;DR

This paper introduces a mean-field model coupling human behavior and climate impact, analyzing equilibria, stability, and convergence, highlighting potential risks of high environmental impact and the need for control strategies.

Contribution

It presents a novel mean-field framework integrating social influence, policy, and costs into climate impact modeling, with analytical and numerical insights.

Findings

System converges to periodic solutions for most initial conditions.

Environmental impact can reach dangerously high levels before stabilization.

Control strategies are needed to prevent high-impact scenarios.

Abstract

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