Dynamics of Holling-type II prey–predator system with a protection zone for prey. Issue 6 (13th April 2022)

• Record Type: Journal Article
• Authors: Zaw Myint, Aung; Wang, Mingxin
• Is Part Of: Applicable analysis. Volume 101:Issue 6(2022)
• Page Start: 1833
• Page End: 1847
• Publication Date: 2022-04-13
• Subjects: Predator–prey model -- global existence -- a priori estimates -- protection zone -- bifurcation -- reaction–diffusion -- Holling-type II functional response; Primary: 92D25 -- 92D50 -- Secondary: 35A01 -- 35B32 -- 35B45 -- 35K57; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1789595
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, a diffusive predator–prey model with Holling type II (Michaelis–Menten) functional response and a protection zone for prey is investigated. Dynamics and steady state solutions of the system are analyzed. We give the a priori estimates and obtain the nonexistence of nonconstant positive solution as the diffusion coefficients are large enough. Moreover, we demonstrate the existence and stability of nonconstant steady state solutions branching from constant semi-trivial solution by using bifurcation theory.