Stability and Bifurcation Analysis in a Discrete Predator–Prey System of Leslie Type with Radio-Dependent Simplified Holling Type IV Functional Response

Autor:	Luyao Lv, Xianyi Li
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	discrete predator–prey system of Leslie type Holling type IV functional response semi-discretization method flip bifurcation Neimark–Sacker bifurcation Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 12, p 1803 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12121803
Popis:	In this paper, we use a semi-discretization method to consider the predator–prey model of Leslie type with ratio-dependent simplified Holling type IV functional response. First, we discuss the existence and stability of the positive fixed point in total parameter space. Subsequently, through using the central manifold theorem and bifurcation theory, we obtain sufficient conditions for the flip bifurcation and Neimark–Sacker bifurcation of this system to occur. Finally, the numerical simulations illustrate the existence of Neimark–Sacker bifurcation and obtain some new dynamical phenomena of the system—the existence of a limit cycle. Corresponding biological meanings are also formulated.
Databáze:	Directory of Open Access Journals
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