主題：Overexploitation Occurs in the Rosenzweig-MacArthur Model with Trigonometric Functional Response
主要內(nèi)容：In this paper, we study a Rosenzweig-MacArthur predator-prey system with a strong Allee effect, and take a predator functional response to the hyperbolic tangent form as trigonometric. We study both the local and global dynamics, and the possible bifurcation is determined according to the variation of the carrying capacity of the prey. An analytic expression is given to determine the criticality of Hopf bifurcation, and the resulting Hopf bifurcation is proved to be supercritical or subcritical. The existence of heteroclinic orbit and Bautin bifurcation are also proved. Biologically speaking, such a heteroclinic cycle always forms a boundary of the region in two parameter space which indicates the breakdown of the system after the invasion of the predator, i.e., overexploitation occurs. Further, numerical simulations are given to demonstrate the theoretical results which include the coexistence of limit cycles and heteroclinic cycles.
專家姓名：徐衍聰
工作單位：杭州師范大學(xué)
專長和學(xué)術(shù)成就：主要從事動(dòng)力系統(tǒng)分支理論、局部斑圖分支及應(yīng)用研究
專家簡介：華東師范大學(xué)應(yīng)用數(shù)學(xué)博士，浙江大學(xué)博士后，杭州師范大學(xué)理學(xué)院數(shù)學(xué)系主任，教授，博士生導(dǎo)師，美國（SIAM）工業(yè)與應(yīng)用數(shù)學(xué)會(huì)員，美國數(shù)學(xué)評論評論員。先后訪問美國布朗大學(xué)、日本京都大學(xué)、德國不萊梅大學(xué)等高校。主要從事動(dòng)力系統(tǒng)分支理論、局部斑圖分支及應(yīng)用研究，主要包括：Dynamical Systems, Dynamics of Patterns, Nonlinear Wave，Homoclinic and Heteroclinic Phenomena等研究工作。主持國家自然科學(xué)基金面上項(xiàng)目、浙江省自然科學(xué)基金， 日本GCOE項(xiàng)目及參與各類基金10余項(xiàng)。
時(shí)間：2020-11-10 19:30:00
地點(diǎn)：騰訊會(huì)議ID： 717 370 392