Open AccessGlobal dynamics of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and prey-taxis
Author(s) -
Jialu Tian,
Ping Liu
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022048
Subject(s) - mathematics , bounded function , functional response , predation , homogeneous , boundary (topology) , lyapunov function , dynamics (music) , stability (learning theory) , mathematical analysis , predator , computer science , nonlinear system , physics , combinatorics , ecology , biology , quantum mechanics , machine learning , acoustics
In this paper, our purpose is to discuss the global dynamics of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and prey-taxis under homogeneous Neumann boundary conditions. First, we derive that the global classical solutions of the system are globally bounded by taking advantage of the Morse's iteration of the parabolic equation, which further arrives at the global existence of classical solutions with a uniform-in-time bound. In addition, we establish the global stability of the spatially homogeneous coexistence steady states under certain conditions on parameters by constructing Lyapunov functionals.