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学术预告:张同华教授谈“Spatio-temporal dynamics near the steady state of a planktonic system”

作者:理学院   点击:0  发布时间:2017-12-05 09:42:29

报告时间:2017925日(周一)下午2:00-3:00

报告地点:下沙校区教学D204(学术报告厅)

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 analyse 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.

报告人简介:

张同华,澳大利亚斯文本科技大学教授。Dr Zhang is a mathematician at Swinburne University of Technology, Australia, who finished his PhD from Shanghai Jiao Tong University in 2005, with a major in Applied Mathematics (Differential Equations and Dynamical Systems). Before joining Swinburne University, he had been working at Curtin University, Perth as a postdoctoral fellow and then a research fellow from August 2005 to October 2010. His current research interests are dynamical system and its application in mathematical biology and modelling of industrial processes. He has published over 90 papers including more than 80 journal articles and one monography on computations of complex industrial systems.