Open AccessA diffusive predator-prey model with generalist predator and time delay
Author(s) -
Ruizhi Yang,
AUTHOR_ID,
Dan Jin,
Wenlong Wang
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022255
Subject(s) - hopf bifurcation , center manifold , mathematics , predator , bifurcation , eigenvalues and eigenvectors , stability (learning theory) , predation , generalist and specialist species , instability , functional response , delay differential equation , mathematical analysis , control theory (sociology) , differential equation , physics , economics , computer science , ecology , biology , mechanics , control (management) , management , quantum mechanics , machine learning , habitat , nonlinear system
Time delay in the resource limitation of the prey is incorporated into a diffusive predator-prey model with generalist predator. By analyzing the eigenvalue spectrum, time delay inducing instability and Hopf bifurcation are investigated. Some conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation. The results suggest that time delay can destabilize the stability of coexisting equilibrium and induce bifurcating periodic solution when it increases through a certain threshold.