生灭随机动力学中的一个集结
On an aggregation in birth-and-death stochastic dynamics
摘要：
考虑具有吸引相互作用的粒子系统的生灭随机动力学。该动力学的启发式生成器具有恒定的出生率和密度相关的递减死亡率。建立了相应的统计动力学模型。利用Vlasov型标度，我们得到了极限介观演化，并证明了这种演化传播混沌。研究了第一个关联函数（种群密度）的非线性非局部动力学方程。一致有界解的存在性以及有界区域内的解的增长和在空间中的扩展。这些解描述了介观系统中的两种状态：调节和聚集。
英文摘要：
We consider birth and death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a non-linear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation.
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