Invasion traveling waves of a three species Lotka–Volterra competitive system with nonlocal dispersal

• Published in: Communications in nonlinear science & numerical simulation 2024-05, Vol.132, p.107939, Article 107939
• Main Authors: Wang, Meng-Lin, Zhang, Guo-Bao, He, Pu
• Format: Article
• Language: English
• Subjects: Competitive systems; Contracting rectangles; Nonlocal dispersal; Traveling waves
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2024.107939

In this paper, we study the invading dynamics of a three species Lotka–Volterra competitive system with nonlocal dispersal. We mainly focus on two situations: (i) two alien species invade one weak native species; (ii) one alien species invades two weak native species. This invasion process can be characterized by the traveling waves connecting two different constant states. By applying Schauder’s fixed point theorem with the help of suitable upper–lower solutions, we prove the existence of two types of traveling waves: one is the traveling wave connecting (0,0,1) at positive infinity, and the other is the traveling wave connecting (0,vc,wc) at positive infinity, where (0,0,1) and (0,vc,wc) are two boundary equilibria of the system. Furthermore, by employing the method of the contracting rectangles, we obtain the asymptotic behavior of two types of traveling waves at negative infinity. Finally, we establish the nonexistence of traveling waves. Our results show that either a strong alien competing species can wipe out the other two species or three weak competing species can coexist. •The more general three species competitive system with nonlocal dispersal is considered.•More types of traveling waves are obtained.•The method of the contracting rectangles is used to prove the stable tail limit of traveling waves.