相互作用种群的演化动力学：考虑非对称性和幂的分类和分析处理
Evolutionary Dynamics of Populations with Conflicting Interactions: Classification and Analytical Treatment Considering Asymmetry and Power
摘要：
演化博弈理论已成功地用于研究系统的动力学，其中许多实体具有竞争性的相互作用。从物理学的角度来看，研究相互作用实体的协调或合作发生的条件是有趣的，无论是自旋，粒子，细菌，动物还是人类。在这里，我们分析的情况下，实体是异质的，特别是两个人口的情况下，相互冲突的相互作用和两种可能的状态。对于这样的系统，将确定用于确定其稳定性的定态解和相关特征值的明确数学公式。这样，四种不同类型的系统动力学可以被分类，并且它们之间的各种相变将被讨论。虽然这些结果从物理学的角度来看是有趣的，但它们也与社会，经济和生物系统相关，因为它们允许人们理解（1）合作的破裂，（2）不同行为（“亚文化”）的共存，（2）共同共享行为（“规范”）的演变，以及（4）极化或冲突的发生。我们指出，规范在社会系统中具有与物理学中的力相似的功能。
英文摘要：
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination or cooperation of interacting entities will occur, be it spins, particles, bacteria, animals, or humans. Here, we analyze the case, where the entities are heterogeneous, particularly the case of two populations with conflicting interactions and two possible states. For such systems, explicit mathematical formulas will be determined for the stationary solutions and the associated eigenvalues, which determine their stability. In this way, four different types of system dynamics can be classified, and the various kinds of phase transitions between them will be discussed. While these results are interesting from a physics point of view, they are also relevant for social, economic, and biological systems, as they allow one to understand conditions for (1) the breakdown of cooperation, (2) the coexistence of different behaviors ("subcultures"), (2) the evolution of commonly shared behaviors ("norms"), and (4) the occurrence of polarization or conflict. We point out that norms have a similar function in social systems that forces have in physics.
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