In this series of lectures, we shall discuss the traveling front solutions for a lattice dynamical system in a monostable 2-species competition system.
The main concerns are the existence and uniqueness of traveling fronts, asymptotic behaviors of wave tails, and the monotonicity of wave profile.
Finally, we apply the results obtained from the lattice dynamical system to the minimal speed of the continuous PDE competition model. We are able to extend the classical result of linear determinacy for the minimal speed to more general cases. This lecture is based on recent joint works with Chang-Hong Wu (in JDE) and Xing Liang (in JDDE).
