Minimal-speed selection of traveling fronts to a three components lattice competition system

Abstract

In this paper, we study the traveling wave problem for a three species lattice competition system with monostable nonlinearity. We are interested in the linear or nonlinear determinacy of the minimal wave speed. Some conditions on the linear determinacy has been obtained in [J.-S. Guo, Y. Wang, C.-H. Wu and C.-C. Wu, The minimal speed of traveling wave solutions for a diffusive three species competition system, Taiwanese J. Math. 19 (2015) 1805–1829]. In this paper, we first provided some general conditions for the linear determinacy. Then, we derive some novel results on the nonlinear determinacy. Finally, some numerical simulations are carried out to illustrate our analytic results. To our knowledge, this may be the first investigation on the nonlinear determinacy of the three species competition system.