Open AccessOn dynamics and stationary pattern formations of a diffusive predator-prey system with hunting cooperation
Author(s) -
Kimun Ryu,
Wonlyul Ko
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022015
Subject(s) - attractor , extinction (optical mineralogy) , predation , neumann boundary condition , steady state (chemistry) , bifurcation , hopf bifurcation , predator , bistability , mathematics , functional response , constant (computer programming) , stability (learning theory) , statistical physics , mathematical analysis , boundary (topology) , control theory (sociology) , nonlinear system , physics , ecology , computer science , biology , chemistry , artificial intelligence , optics , control (management) , quantum mechanics , machine learning , programming language
The current paper provides a qualitative study of a diffusive predator-prey system with a hunting-cooperation functional response under homogeneous Neumann boundary conditions. The considered functional response explains a behavioral mechanism in which predators search for and hunt their prey cooperatively. We investigate the global attractor for nonnegative time-dependent solutions to the system and the nonpersistence leading to the extinction of the predator species in the system. Moreover, we study the local stability at all feasible nonnegative constant steady states and the occurrence of Hopf bifurcation (i.e., the existence of time-periodic orbits) in the system. Finally, we study the existence and nonexistence of nonconstant positive steady states in the system, and the limiting behavior of the positive steady states according to the diffusion rate. Through this study, we observe interesting results, such as bistability, extinction of the predator species induced by a large consumption rate, and stationary patterns in the system with hunting cooperation in predators.