标题： 具有游戏动力相互作用的增殖活性磁盘 显示英文标题

标题： Proliferating active disks with game dynamical interaction

摘要： 我们研究了一个具有博弈论相互作用的自推进、增殖的有限尺寸圆盘系统，其中生长率取决于局部种群组成。 我们分析这些相互作用如何影响空间分布、共存和灭绝。 三种情景出现：(i) 稳定共存，具有均匀混合分布，(ii) 双稳态，结果取决于初始条件，以及 (iii) 主导，其中一种物种总是击败另一种。 我们进一步表明，活动增强了共存中的空间混合，并在主导和双稳态中减少了灭绝时间。 此外，更强的相互作用促进了共存，而在后两种情况下加速了灭绝。 通过改变扩散率、活动性和相互作用强度，我们展示了运动和空间限制如何影响种群动态。 显示英文摘要

摘要： We study a system of self-propelled, proliferating finite-size disks with game-theoretical interactions, where growth rates depend on local population composition. We analyze how these interactions influence spatial distribution, coexistence, and extinction. Three scenarios emerge: (i) stable coexistence with well-mixed distributions, (ii) bistability, where the outcome depends on initial conditions, and (iii) dominance, where one species always outcompetes the other. We further show that activity enhances spatial mixing in coexistence and reduces extinction times in both dominance and bistability. Additionally, stronger interactions promote coexistence while accelerating extinction in the latter two regimes. By varying diffusivity, activity, and interaction strength, we show how movement and spatial constraints affect population dynamics.