Open AccessCodimension two 1:1 strong resonance bifurcation in a discrete predator-prey model with Holling Ⅳ functional response
Author(s) -
Mianjian Ruan,
Chang Li,
Xianyi Li
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.2022174
Subject(s) - functional response , codimension , mathematics , bifurcation , center manifold , predation , transcritical bifurcation , saddle node bifurcation , predator , bifurcation theory , discrete time and continuous time , mathematical analysis , pure mathematics , hopf bifurcation , physics , nonlinear system , statistics , biology , quantum mechanics , paleontology
In this paper we revisit a discrete predator-prey model with Holling Ⅳ functional response. By using the method of semidiscretization, we obtain new discrete version of this predator-prey model. Some new results, besides its stability of all fixed points and the transcritical bifurcation, mainly for codimension two 1:1 strong resonance bifurcation, are derived by using the center manifold theorem and bifurcation theory, showing that this system possesses complicate dynamical properties.