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學術預告:張同華教授談“Spatio-temporal dynamics near the steady state of a planktonic system”

來源 : 理學院     作者 : 理學院     時間 : 2017-09-18     

報告人:張同華,澳大利亞斯文本科技大學教授

報告題目:Spatio-temporal dynamics near the steady state of a planktonic system

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 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.

報告時間:2017年9月25日(周一)下午2:00-3:00

報告地點:下沙校區教學D樓204室(學術報告廳)

報告人簡介: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.


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