Emergent Dynamic Behaviors in Complex Social and Ecological Systems: a Co-Evolutionary Game-Theoretic Approach

This thesis investigates emergent dynamic behaviors in some classes of social and ecological systems from the co-evolutionary game-theoretic perspective. These systems under study are closely related to long-standing issues in the social, ecological and economic sciences, which include, but not limited to, the decision-making, social cultural evolution, plant nutrient acquisition, global climate change, and resource harvesting problems. We use a set of relatively simple and tractable evolutionary models to study the dynamics by using mathematical tools from game theory, dynamical systems theory, and control theory. The influence of distinct factors on systems' behaviors, such as mutations, time-scale separations, and payoff variations, are investigated in depth. The studied social and ecological systems can exhibit diverse types of dynamic behaviors. In addition to convergence to steady states, we show that oscillations can be commonly expected. Moreover, the oscillatory behaviors can be further categorized into several types, which mathematically correspond to (neutrally) periodic orbits, heteroclinic orbits, and (stable or unstable) limit cycles. The research presented in this thesis reveals that the co-evolutionary approach enables us to investigate, identify, and forecast dynamic behaviors in social and ecological systems, which in turn has substantial implications for the management and control of such systems.