走向现代数学学术报告 - 袁胜兰助理教授（No. 651）

题目：Bifurcation and chaotic behaviour in stochastic Rosenzweig-MacArthur prey-predator model with non-Gaussian stable Lévy noise

报告人：袁胜兰 助理教授（大湾区大学 筹）

时间；2023年10月19日，16:30

地点：东海岸-E教514

摘要：We perform dynamical analysis on a stochastic Rosenzweig–MacArthur model driven by α-stable Lévy motion. We analyze the existence of the equilibrium points, and provide a clear illustration of their stability. It is shown that the nonlinear model has at most three equilibrium points. If the coexistence equilibrium exists, it is asymptotically stable attracting all nearby trajectories. The phase portraits are drawn to gain useful insights into the dynamical underpinnings of prey–predator interaction. Specifically, we present a transcritical bifurcation curve at which system bifurcates. The stationary probability density is characterized by the non-local Fokker–Planck equation and confirmed by some numerical simulations. By applying Monte Carlo method and using statistical data, we plot a substantial number of simulated trajectories for stochastic system as parameter varies. For initial conditions that are arbitrarily close to the origin, parameter changes in noise terms can lead to significantly different future paths or trajectories with variations, which reflect chaotic behavior in mutualistically interacting two-species prey–predator system subject to stochastic influence. This is the joint work with Zibo Wang.

报告人简介：袁胜兰，大湾区大学（筹）理学院助理教授。2017年9月至2018年8月前往德国德累斯顿工业大学CSC联合培养博士，2019年获华中科技大学博士学位。先后在华中科技大学人工智能与自动化学院从事博士后和德国奥格斯堡大学任助理研究员。研究方向为Lévy过程驱动的随机动力系统、量子力学、统计物理和随机分析。近五年在SIAM Journal on Applied Dynamical Systems、Journal of Statistical Mechanics、Analysis and Applications等国际重要期刊上发表15篇学术论文。