论文标题
随机Lotka-Volterra系统中的慢速动力学
Slow-fast dynamics in stochastic Lotka-Volterra systems
论文作者
论文摘要
我们研究了具有三态循环个体行为和参数依赖性过渡速率的随机粒子系统家族的大种群动力学。在短时间内，动力学事实证明是由一个可集成的哈密顿系统近似的，该系统的相空间是由周期性轨迹散发的。此功能建议考虑由于快速振荡而导致的长期过程的有效动力学。我们在较大的人口限制中建立了这一过程的收敛，以限制显式随机微分方程的解决方案。值得注意的是，这种平均现象与固定措施的收敛相辅相成。平均的证据遵循Stroock-Varadhan方法来解决Martingale问题，并依赖于对系统动力学特征的精细分析。
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated by an integrable Hamiltonian system whose phase space is foliated by periodic trajectories. This feature suggests to consider the effective dynamics of the long-term process that results from averaging over the rapid oscillations. We establish the convergence of this process in the large population limit to the solutions of an explicit stochastic differential equation. Remarkably, this averaging phenomenon is complemented by the convergence of stationary measures. The proof of averaging follows the Stroock-Varadhan approach to martingale problems and relies on a fine analysis of the system's dynamical features.
