报告题目：一个浮游生物系统平稳态附近的时空动力学
Spatio-temporal dynamics near the steady state of a planktonic system
报告时间：2018年7月3日（星期二）下午14:30-15:30
报告地点：理学院二楼会议室
报告人：张同华，博士。2005年在上海交通大学应用数学专业博士毕业，后到西奥科廷大学从事博士后研究工作。现在是澳大利亚斯文本大学任教，应用数学专业博士生导师。主要研究领域：微分方程定型理论和分支理论，及其在科学和工程过程中的应用。
报告摘要：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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