Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect. (29th December 2020)

• Record Type: Journal Article
• Authors: Feng, Xiaozhou; Sun, Hao; Xiao, Yangfan; Xiao, Feng
• Other Names: Guo Songbai Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-12-29
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/8899114
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : This paper investigates the diffusive predator-prey system with nonmonotonic functional response and fear effect. Firstly, we discussed the stability of the equilibrium solution for a corresponding ODE system. Secondly, we established a priori positive upper and lower bounds for the positive solutions of the PDE system. Thirdly, sufficient conditions for the local asymptotical stability of two positive equilibrium solutions of the system are given by using the method of eigenvalue spectrum analysis of linearization operator. Finally, the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray–Schauder degree theory and Poincaré inequality.