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

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 t...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-06, Vol.12 (12), p.1803
Main Authors: Lv, Luyao, Li, Xianyi
Format: Article
Language:English
Subjects:
Bifurcation theory
discrete predator–prey system of Leslie type
Ecology
Ecosystems
flip bifurcation
Holling type IV functional response
Neimark–Sacker bifurcation
Numerical analysis
Predator-prey simulation
Predators
semi-discretization method
Simulation methods
Stability
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12121803