Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting

Abstract

This paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder's fixed point theorem, we show that there exists a positive constant $ c^* $ such that the system possesses a traveling wave solution for any given $ c > c^* $. Moreover, the asymptotic behavior of traveling wave solution at infinity is obtained by the contracting rectangles method. The existence of traveling wave solution for $ c = c^* $ is established by means of Corduneanu's theorem. The nonexistence of traveling wave solution in the case of $ c < c^* $ is also discussed.

Keywords

• predator-prey model
• beddington-deangelis functional response
• traveling wave solution
• nonlocal dispersal equation
• upper-lower solutions
• asymptotic behavior