報告題目：一個浮遊生物系統平穩態附近的時空動力學
Spatio-temporal dynamics near the steady state of a planktonic system
報告時間：2018年7月3日（星期二）下午14:30-15:30
報告地點：必一体育平台二樓會議室
報告人：張同華，博士。2005年在上海交通大學應用數學專業博士畢業，後到西奧科廷大學從事博士後研究工作。現在是澳大利亞斯文本大學任教，應用數學專業博士生導師。主要研究領域：微分方程定型理論和分支理論，及其在科學和工程過程中的應用。
報告摘要：The study of spatio-temporal behaviour of ecological systems is fundamentally important as it can provide deep understanding of species interaction and predict the effects of environmental changes. In this paper, we first propose a spatial model with prey taxis for planktonic systems, in which we also consider the herb behaviour in prey and effect of the hyperbolic mortality rate. Applying the homogeneous Neumann boundary condition to the model and using prey- tactic sensitivity coefficient as bifurcation parameter, we then detailedly analyze the stability and bifurcation of the steady state of the system: firstly, we carry out a study of the equilibrium bifurcation, showing the occurrence of fold bifurcation, Hopf bifurcation and the BT bifurcation; then by using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter, we investigate the Turing-Hopf bifurcation, obtaining a branch of stable non-constant solutions bifurcating from the positive equilibrium, and our results show that prey- taxis can yield the occurrence of spatio-temporal patterns; finally, numerical simulations are carried out to illustrate our theoretical results, showing the existence of a two-peak periodic solution when the prey-tactic sensitivity coefficient is away from the critical value.
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