题目：Reaction-Diffusion Model with Nonlocal Effects Modeling Tidal Marsh Spatial Patterning and Pollen Tube Tip Growth
报告人：Prof. Junping Shi （College of William and Mary）
Abstract: We will talk about two recent work: 1. A reaction-diffusion model with nonlocal interactions between ribbed mussels, marsh grass and sediment is proposed. Mussel-grass aggregating behavior is suggested to be a result of nonlocal density-dependent interactions between mussels. The model is a reaction-diffusion system with cooperative kinetic dynamics which is outside of the regime of classical Turing instability mechanism, but the nonlocal interaction causes the generation of spatial patterns. The nonlocal model can be approximated by a bi-harmonic PDE, which produces analytic results marching the numerical simulation of full nonlocal model. 2. A reaction-diffusion model is proposed to describe the evolution of spatial distributions of ROP1 and calcium on the pollen tube tip. The cytoplasmic ROP1 activate ROP1 on the membrane and the calcium ions inhibit ROP1, while ROP1 controls calcium influx with a time delay. Lateral movement of molecules on the membrane are depicted by diffusion. It is shown that bistable or oscillatory dynamics could exist even in the non-spatial model, and time delay can also promote oscillation. Stationary and oscillatory spatiotemporal patterns are found in the full spatial model which resemble the experimental data of pollen tube tip growth.
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