Global dynamics of a Lotka-Volterra type prey–predator model with diffusion and predator-taxis. Issue 16 (2nd November 2022)

• Record Type: Journal Article
• Authors: Yoon, Changwook
• Is Part Of: Applicable analysis. Volume 101:Issue 16(2022)
• Page Start: 5557
• Page End: 5570
• Publication Date: 2022-11-02
• Subjects: 23783; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1898598
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This paper studies a reaction–advection–diffusion prey–predator system in one spatial dimension. Adapting the Lotka–Volterra-type functional response, we prove the global existence and boundedness of solutions of the system in a bounded open interval. In view of asymptotic behavior of solutions, we show that if the predation is weak, the semi-trivial steady state at which prey only survive is globally asymptotically stable. In case of strong predation, the positive steady state is globally asymptotically stable when the predator-taxis is weak.