研究复杂网络上演化博弈在不同演化动态下合作演化形成机理及合作演化的控制策略，旨在理解人类合作行为是怎样产生和发展的。给出不同复杂网络上演化博弈的邻接矩阵表示与集值映射表示。建立无限种群基于粒子群优化算法的演化动态和基于数据科学算法的最优反应动态的演化动态及其动力学方程并探讨与邻接矩阵的关系，分析动力学方程的合作动态稳定条件与特性，揭示动力学系统动态稳定点与博弈模型演化稳定策略的关系；构建有限种群基于Moran过程和基于Wright-Fisher过程的随机演化动态的状态转移矩阵及其与邻接矩阵的关系，分析这两种随机演化动态的扎根概率与条件扎根时间的极限分布，揭示极限分布的合作特性及与随机稳定均衡的关系；构建策略-结构共演化的演化动态及其动力学关系，分析合作动态稳定特性。设计复杂网络上演化博弈在不同演化动态下促合作演化的激励机制和控制策略。成果将为解释结构化种群合作是怎样形成和发展的提供科学方法.

This project aims at understanding how human cooperative behaviors are generated and developed from the perspective of formation mechanisms and control strategies of cooperation evolution on complex networks under different evolutionary dynamics. We will give the representation of adjacency matrix and set-valued mapping for evolutionary game on different complex networks. In the infinite population, we will establish evolution dynamics of evolutionary game on complex networks based on particle swarm optimization algorithm and best　response　dynamics based on data science algorithm and its dynamic equations, and explore their relationship with adjacency matrix. We will also analyze stability conditions and characteristics of the dynamic equations and reveal the relationship between dynamic stable points of system and evolutionary stable strategies of game models. In the finite population, we will establish the state transition matrix of stochastic evolutionary dynamics based on Moran process and Wright-Fisher process and its relationship with the adjacency matrix, and study the limit distribution of fixation probability and conditional fixation time in these two kinds of stochastic evolution dynamics. We will also reveal the relationship between limit distribution of cooperation characteristics and stochastic stable equilibrium. We will set up the evolution dynamics of strategy-structure coevolution, and analyze the dynamic stability characteristics of cooperation. The incentive mechanisms and control strategies of evolutionary game on complex networks are designed to promote cooperation evolution under different evolutionary dynamics. The results will provide scientific methods to explain how the cooperation of structured population is formed and developed.