Propagation dynamics of a Lotka–Volterra competition model with stage structure in time–space periodic environment. (October 2022) - Zhao, Xiao; Yuan, Rong
Abstract: We consider a diffusive Lotka–Volterra competition model with stage structure and time–space periodic habitats. Firstly, we investigate that the system has two periodic semi-trivial solutions ( u ∗ ( t, x ), 0 ) and ( 0, v ∗ ( t, x ) ) . Next, the existence of the principal eigenvalue for the eigenvalue problem associated with a linear time–space periodic reaction–diffusion cooperative system with time delay is established. By using eigenvalue functions and semi-trivial solutions, we construct upper and lower solutions. Then by Schauder's fixed point, there is a pulsating wave solution ( U ( t, x, x + c t ), V ( t, x, x + c t ) ) connecting ( 0, v ∗ ( t, x ) ) and ( u ∗ ( t, x ), 0 ) .