Speaker: Prof Junping Shi (College of William and Mary)
Title: Instability, bifurcation and pattern formation in models with chemotaxis, advection and delay
Time: 2013-03-28 (Thu.)  15:00 - 16:00
Abstract: In an evolution equation, a constant equilibrium is often stable if the perturbation is also a constant one, hence it is dynamically stable with respect to an ODE dynamics. More realistic models often include the effect of spatial dispersal such as diffusion or advection. In the classical Turing reaction-diffusion model, an instability is caused by diffusion with different diffusion coefficients, and it generates non-constant steady state solutions via a bifurcation. In this talk, we show that time-periodic patterns arise in several structured mathematical models: (i) a reaction-diffusion model with attractive and repulsive chemotaxis, (ii) an advection-reaction-diffusion model of vegetation patterns, and (iii) general planar systems of delay differential equations. In all the cases, Hopf bifurcations occur so oscillatory states emerge as the result of instability. The talk is based on joint work with (i) Ping Liu, Zhian Wang, (ii) Jun Zhou, and (iii) Shanshan Chen and Junjie Wei.
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