报告人：Peter van Heijster教授

报告题目：Transition from Turing instability to large periodic solutions in a reaction-diffusion system

摘要：Analytically tracking patterns emerging from a Turing small amplitude instability to large amplitude patterns remains a challenge as no general theory is available. In this talk, we consider a three-component reaction-diffusion system and develop an analytical understanding of periodic patterns emerging from a Turing instability using spatial geometric singular perturbation theory. The system has a single singularly perturbed component known as a fast variable. We show analytically that after the initial Turing instability, spatially periodic patterns evolve into a small amplitude spike in the fast variable whose amplitude grows as one moves away from onset. This is followed by a secondary transition where the spike in the fast variable widens, its periodic pattern develops two sharp transitions between two flat states and the amplitudes of the other variables grow. The final type of transition we uncover analytically is where the flat states of the fast variable develop structure in the periodic pattern. Numerically, we show that the structure allows the periodic patterns to undergo a succession of Turing instabilities repeating the transition processes described above. This leads to the development of more complicated periodic patterns and snaking-like behaviour.

报告时间：2023年1月11日16:30-18:00

报告地点：线上。详细信息请联系李一飞老师(邮箱：yifeili@hit.edu.cn)。

报告人简介：Prof. dr. Peter van Heijster worked as a postdoctoral associate at Boston University in the USA before commencing in august 2012 at QUT as an assistant, and later associate, professor. In September 2020 he started at the WUR as the Chair of Mathematics in Biometris. He is an applied analyst and his research focusses on nonlinear dynamics, and in particular on understanding pattern formation. The aim of his research is to get a better understanding of the pattern formation processes in paradigmatic mathematical models and to apply the new insights to more biologically-realistic models. He is particularly interested in the theoretical and mathematical underpinnings of the effects of heterogeneities on pattern formation processes.