Abstract:

Pulsating wave has a property of recurrence up to certain time and space shifts. It plays an important role in the study of propagation dynamics for reaction-diffusion equations in time or space periodic media, but evidently it may not exist in time-space periodic media. In this talk, for a class of dynamical systems admitting the comparison principle, we construct a kind of generalized transition wave that was introduced by H. Berestycki and F. Hamel in 2012. It turns out that the constructed transition wave has a property of almost recurrence. The "almost" property reflects the joint influence of time and space periodicities. This talk is based on a joint work with Xiao Yu and Xiaoqiang Zhao.