“数理论坛”83期：Spatial dynamics of a nonlocal model with periodic delay and competition

报告题目

Spatial dynamics of a nonlocal model   with periodic delay and competition

报告时间

2019年3月27日（周三）16:00—17:00

报告地点

东区教学科研综合楼A座1404

报告人

张亮 （兰州大学）

报告人

简介

张亮，2016年毕业于兰州大学数学与统计学院，获理学博士学位，主要从事微分方程与应用动力系统研究，已在Trans. Amer. Math. Soc.、J.   Differential Equations、J. Dynam.   Differential Equations、Z. Angew.   Math. Phys.等SCI期刊上发表学术论文十余篇，并于2017年获批国家自然科学基金青年科学基金项目。

报告摘要

Each species is subject to various biotic   and abiotic factors during growth. In this talk, we formulates a   deterministic model with the consideration of various factors regulating   population growth such as age-dependent birth and death rates, spatial   movements, seasonal variations, intra-specific competition and time-varying   maturation simultaneously. The model takes the form of two coupled   reaction-diffusion equations with time-dependent delays, which bring novel   challenges to the theoretical analysis. Then the model is analyzed when   competition among immatures is negligible, in which situation one equation   for the adult population density is decoupled. The well-posedness of the   system is established and the basic reproduction number R0 is defined and   shown to determine the global attractivity of either the zero equilibrium   (when R_0<1) or a positive periodic solution (R_0 > 1) by using the   dynamical system approach on an appropriate phase space. When the immature   intra-specific competition is included and the immature diffusion rate is   negligible, the model is neither cooperative (where the comparison principle   holds) nor reducible to a   single equation. In this case, the threshold dynamics about the population   extinction and uniform persistence are established by using the newly defined   basic reproduction number R_0 as a threshold index. This talk is based on a   joint work with Dr. Kaihui Liu, Prof. Yijun Lou and Prof. Zhi-Cheng Wang.

邀请人

王佳兵 特任副教授  

2019 年3月 26 日

学院

审核意见

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