On the morning of August 12. Professor Junping Shi from College of William & Mary gave an online report entitled “Effect of nonlocal interaction or dispersal on the spatial-temporal pattern formation of reaction-diffusion systems”. Huaqing Sun hosted this report, teachers and graduate students of our school attended this report online.

In reaction-diffusion models describing biological and chemical interactions, some dispersal and interaction can be of nonlocal nature. We show that 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. We will show that when a nonlocal dispersal occurs instead of classical diffusion, how the mechanism of Turing diffusion-induced instability and pattern formation changes. Example from activator-inhibitor with nonlocal dispersal and a marsh grass model will be used to demonstrate pattern formation. From this talk teachers and students all obtained better understandings of this area, and benefit a lot.

The successful holding of this report has strengthened atmosphere in researching probability theory in our school. and deepened the friendship and cooperation between the two sides.