复杂系统演化中的若干关键问题研究

Exploring the emergence of cooperation in complex systems will be in favor of the design of interaction mechanisms as well as the coordination of the components’ behaviors. It thus has important theoretical significance and engineering value for some practical problems in complex systems, such as the coordinated control of swarm robot systems and the formation control of unmanned aerial vehicles. This project is mainly concentrated on some key topics in the evolution of complex systems by virtue of the evolutionary game theory. (i) We investigate the evolution of cooperation in structured populations with interaction stochasticity, specify the conditions for cooperation to flourish, and reveal the effects of the coordination of interaction stochasticity and spatial structures on the evolution of cooperation. (ii) We analyze the evolutionary stability of cooperation in structured populations with stochastic social dilemmas, and study the influences of stochastic social dilemmas on cooperation in structured populations. (iii) We propose the endogenous punishment based on democratic voting, explore the evolution of cooperation under the endogenous punishment, and specify the conditions under which cooperation is favored. (iv) We investigate the evolutionary dynamics of antagonistic symbiosis in asymmetric group-structured populations with heterogeneity, and analyze the effects of the heterogeneity in update rates, mutation rates, and interaction rates on antagonistic symbiosis when intra-group interactions are considered. (v) Finally, we focus the attention on the application of evolutionary game theory in the coordinated control of stochastic multi-agent systems, provide the feasible theoretical framework, and pave the way for the application of evolutionary game theory in practical complex systems.

探索复杂系统中的合作演化动力学，有利于设计实际系统中个体交互的规则并协调个体的行为，从而对群体机器人协同控制、无人机编队控制等实际问题具有重要的理论意义和应用价值。本项目拟基于演化博弈论对复杂系统演化过程中的若干关键问题进行研究。(i) 研究随机交互下结构种群中的合作演化，给出合作涌现的阈值条件，并揭示交互随机性与结构特性的耦合对合作演化的影响；(ii) 分析在随机博弈下结构种群中的合作演化稳定性，并阐明随机博弈在结构种群中对合作涌现的作用；(iii) 提出基于民主决策的内生惩罚机制，研究内生惩罚下的合作演化，并给出合作涌现的阈值条件；(iv) 探索异质性条件下非对称群组结构种群中的对抗共生演化动力学，分析在群组内部交互下群组间更新速率、变异率、以及组内交互速率的异质性对对抗共生演化的影响；(v) 运用所得演化博弈论的研究结果探讨随机多智能体系统中的协同控制问题，并给出可行的理论框架。

探索复杂系统中合作行为的演化动力学，有利于设计实际系统中个体交互的规则并协调个体的行为，从而对群体机器人协同控制、无人机编队控制等实际问题具有重要的理论意义和应用价值。本课题基于演化博弈论对复杂系统中合作行为的动态演化展开研究并揭示了合作行为的涌现机理。首先，探索了复杂系统中合作行为在随机交互环境下的演化动力学，给出了规则网络中合作行为涌现的阈值条件，并分析了规则网络的结构特性对该条件下合作演化的影响。其次，建立了基于税制的制度激励机制，并在此基础上对比研究了在完美和不完美观测环境下制度激励对合作涌现的影响；再次，提出了基于群体决策的一致性惩罚机制，研究了复杂系统中合作行为在该激励机制下的涌现，对比分析了基于不同决策形式的惩罚机制对合作演化的影响，明确了个体对惩罚机制的偏好以及趋同性作用下的合作演化，并探索了当系统存在偏好颠倒现象时合作行为的演化动力学。最后，针对有限资源环境，探索了资源有限性与一致性激励机制耦合作用下的合作演化并给出了合作行为涌现的阈值条件。