报告题目：Nonlinear Stochastic Difference Equations

报告人： 王海燕

报告时间：2026年7月6日上午9点

报告地点：仙林校区自动化学科楼321会议室

主办单位：麻豆av 、科学技术处

报告人简介：

王海燕现任美国亚利桑那州立大学（Arizona State University）数学与自然科学学院教授。1997年获密歇根州立大学数学博士学位和计算机科学硕士学位。其研究领域包括应用数学、随机差分方程、微分方程、数学建模、数据科学、量子计算、人工智能和生物数学等。在国际学术期刊发表论文百余篇。著有《Mathematical Methods in Data Science》和《Modeling Information Diffusion in Online Social Networks with Partial Differential Equations》等学术专著。近年来，他积极开展随机差分方程在种群动力学和复杂系统中的应用研究，以及量子机器学习和大语言模型（LLM）相关研究，致力于推动数学、计算、人工智能与数据科学的交叉融合。

报告摘要：

The Logistic and Ricker equations are cornerstone models for understanding nonlinear biological dynamics. This talk explores the stochastic discrete-time versions of these models, comparing their behavior to well-known classical deterministic models and continuous-time stochastic differential equations (SDEs).

Mathematical analysis of the stationary distributions at equilibrium reveals a bifurcation structure with two branches of alternative stable states. To capture long-term population behavior, we demonstrate the validity of the Gaussian/Gamma moment-closure approximation and derive a closed system of difference equations for the mean and variance. We establish necessary/sufficient conditions for the existence, uniqueness, and local stability of the equilibrium. These results highlight a fundamental biological trade-off: the balance between the stabilizing force of intrinsic growth rates and the destabilizing impact of environmental variability.