[PAST EVENT] Mathematics Colloquium: Junping Shi (William & Mary)
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- Open to the public
Title: Effect of spatial average on the spatial-temporal pattern formation of reaction-diffusion systems
Abstract: In reaction-diffusion models describing biological and chemical interactions, some dispersal and interaction can be of nonlocal nature. First we show that in some models from cellular biology or ecology depending on the spatial average of density functions instead of local density functions, such nonlocal spatial average can induce instability of constant steady state, which is different from classical Turing instability. In particular, for systems of two equations containing spatial averages, spatially non-homogeneous time-periodic orbits could occur through bifurcations from the constant steady state. Examples from a nonlocal predator-prey model and a pollen tube tip model will be used to demonstrate such bifurcations. In another direction, we show that when a averaging nonlocal dispersal occurs instead of classical diffusion, how the mechanism of Turing diffusion-induced instability and pattern formation changes.