Speed determinacy of travelling waves for a three-component lattice Lotka-Volterra competition system

In this paper, the invasive speed selection of the monostable travelling wave for a three-component lattice Lotka-Volterra competition system is studied via the upper and lower solution method, as well as the comparison principle. By constructing several special upper and lower solutions, we establish sufficient conditions such that the linear or nonlinear selection is realized.

Bistable wave speed of the Lotka-Volterra competition model

This work deals with the speed sign of travelling waves to the Lotka-Volterra model with diffusion and bistable nonlinearity. We obtain new conditions for the determinacy of the sign of the bistable wave speed by constructing upper or lower solutions with an inside parameter to be adjusted. The established conditions improve or supplement the results in the references and give insight into the combined effect of system parameters on the propagation direction of the bistable wave.