报告题目：How stochasticity and discretization affect population dynamics: from two discrete pest control models

报告时间：2026年9月20日下午15:00

报告地点：南湖校区郭力楼二楼会议室1256室

主办单位：红杏视频

报告人：刘兵

报告人简介：刘兵，鞍山师范学院数学学院院长、三级教授、辽宁科技大学博士生导师，辽宁省“百千万人才工程”百人层次人选，辽宁省教学名师，辽宁省青年科技奖获得者，鞍山市首批突出贡献专家，鞍山市“钢都英才计划”C类地方领军人才。主要研究方向为生物数学和数学教育。目前为中国生物数学会常务理事，国家自然科学基金同行评议专家，IJB编委。在国内外学术期刊发表论文100余篇，其中SCI检索50余篇，数学教育类论文10余篇，被人大复印资料转载一篇；主持国家自然科学基金项目5项，入选辽宁省高等学校优秀人才支持计划项目。

摘要：Considering that it is often subject to various stochastic white noise during the process of integrated pest management, and discrete models are more accurate in describing the situations where the successive generations of many species in nature are non-overlapping and the data of biological samples are usually collected in discrete time, this report presents and analyzes two distinct stochastic discrete models to investigate the effects of stochastic white noise on population dynamics. The first model develop a stochastic discrete crop-pest-natural enemy model using the Positive and Elementary Stable Nonstandard method, which preserves the positivity and stability of equilibria from the original continuous system, independent of the time step size. We provide sufficient conditions for the stability in probability of the pest-extinction and positive equilibria. Numerical simulations demonstrate that unlike the Euler method, which diverges with large step sizes, the PESN discretization exhibits numerical stability and better preserves the dynamical properties of the correponding deterministic discrete model. The second model introduces multiplicative white noise, modeled as independent double-truncated standard normal sequences, directly affecting the pest growth rate and natural enemy mortality. For this model, we establish the positivity and boundedness of solutions and derive sufficient conditions for pest extinction. Our analysis reveals that while low-intensity noise does not alter the population's fate, excessively high noise intensity can drive a population to extinction.