Resumen de Minimal-Speed Selection to a Lotka–Volterra Competition System with Local Versus Nonlocal Diffusions and Cubic Nonlinearity

Jiali Zhan, Jiding Liao, Hongyong Wang

• In this paper, the minimal-speed selection mechanism to a Lotka–Volterra type of model with local versus nonlocal diffusions and cubic nonlinearity is considered.

  By using comparison principle and upper-lower solution method, general criteria for both linear and nonlinear selection of the minimal wave speed are derived. Based on these results, several explicit conditions for determining the linear selection of the minimal wave speed are obtained via the constructions of various upper solutions.

  These conditions can help us to confirm that the species will spread with the speed of a linearised system and take an insight into thresholds for different model parameters.

  Moreover, it is found that the model with cubic nonlinearity causes a very different mechanism compared to the one caused by quadratic nonlinearity. For example, the linear selection can be realized when the diffusion strength is in an infinite interval for the model with cubic nonlinearity. Finally, it should be pointed out that concrete conditions for nonlinear selection are not obtained due to the failure of construction of a lower solution, and are left for further work.