Research on the Dynamical Behaviors of Discrete and Continuous Dynamical Systems(2/3)

In this project, we will investigate the dynamical behaviours of solutions for some discreteand continuous dynamical systems. One of the main topics is the existence, uniqueness,asymptotic behaviour and stability of traveling wave solutions for various discrete and continuousdynamical systems. In addition, we are also interested in studying the attractivity(global stability) of the equilibria, and the existence of entire solutions which arise from theinteraction of traveling fronts with different wave speeds. For examples, we plan to continueour investigations on the following specific problems from the lattice dynamical systems andreaction-diffusion systems.