应云顶国际4008服务平台邀请，日本青山学院大学（Aoyama Gakuin University）数学与物理系教授Yasuhiro TAKEUCHI于9月3日-10日来我校进行学术交流并作系列学术报告。

题 目：Revisited: Rosenzweig-MacArthur Model  and Lotka-Volterra Prey-predator Model

时 间：2017年9月6日（周三）， 上午10：00～12：00

地 点：理科楼408会议室

摘 要：

Maturation time delay for the predators is introduced in prey-predator models to implicitly model the stage-structure of predators. Most of the prey-predator models with maturation delay are known to exhibit destabilization of coexistence steady-state. Discrete time delay induced destabilization is a common finding, however, this is due to the introduction of time delay with lack of ecological justification. The main objective of the present work is to show the stabilizing role of maturation delay for a class of delayed prey-predator model. To be specific, we consider prey-predator models with strong and weak Allee effects in prey growth and Michaelis-Menten type functional response. We provide ecological justification for the introduction of maturation delay parameter in predator's growth equation. We obtain the conditions for stable and oscillatory coexistence of prey and their specialist predator in case of strong as well as weak Allee effect for non-delayed and delayed models. Apart from the analytical results for the models under consideration, we perform extensive numerical simulations to construct the relevant bifurcation diagrams. Our analytical and supportive numerical findings reveal that delay is not always a destabilizing factor rather the stable coexistence in the presence of time delay depends upon the formulation of the delayed model. The biological implications of the current investigation are provided in the conclusion section. We also explain the validity of obtained results for other types of prey-predator models with a specialist predator.

报告人简介：

Yasuhiro TAKEUCHI教授在日本京都大学获得博士学位。主要从事生物数学和传染病动力学领域的研究，尤其是时滞微分方程理论及其在生态系统和传染病中的应用研究。Yasuhiro TAKEUCHI教授曾担任日本生物数学会主席，目前担任国际杂志《Mathematical Biosciences and Engineering》和《Japan Journal of Industrial and Applied Mathematics》的副主编，同时也是《Journal of Theoretical Biology》、《Journal of Biological Dynamics》等杂志的编委。出版了专著8部，已经在《SIAM Journal on Applied Mathematics》、《Journal of Theoretical Biology》、《Bulletin of Mathematical Biology》、《Journal of Mathematical Biology》、《PLoS ONE》、《Mathematical Biosciences》等国际权威期刊上发表学术论文170多篇。主持日本自然科学基金项目10多项。

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