Changrong Zhu | Searcharxiv

arXiv2025

Complex dynamics of a predator-prey model with constant-yield prey harvesting and Allee effect in predator

This paper investigates the dynamical behaviors of a Holling type I Leslie-Gower predator-prey model where the predator exhibits an Allee effect and is subjected to constant harvesting. The model demonstrates three types of equilibrium points under different parameter conditions, which could be either stable or unstable nodes (foci), saddle nodes, weak centers, or cusps. The system exhibits a saddle-node bifurcation near the saddle-node point and a Hopf bifurcation near the weak center. By calculating the first Lyapunov coefficient, the conditions for the occurrence of both supercritical and subcritical Hopf bifurcations are derived. Finally, it is proven that when the predator growth rate and the prey capture coefficient vary within a specific small neighborhood, the system undergoes a codimension-2 Bogdanov-Takens bifurcation near the cusp point.

math.DS↗

arXiv2025

A study on a class of predator-prey models with Allee effect

This paper investigates the dynamical behaviors of a Holling type I Leslie-Gower predator-prey model where the predator exhibits an Allee effect and is subjected to constant harvesting. The model demonstrates three types of equilibrium points under different parameter conditions, which could be either stable or unstable nodes (foci), saddle nodes, weak centers, or cusps. The system exhibits a saddle-node bifurcation near the saddle-node point and a Hopf bifurcation near the weak center. By calculating the first Lyapunov coefficient, the conditions for the occurrence of both supercritical and subcritical Hopf bifurcations are derived. Finally, it is proven that when the predator growth rate and the prey capture coefficient vary within a specific small neighborhood, the system undergoes a codimension-2 Bogdanov-Takens bifurcation near the cusp point.

math.DS↗

arXiv2023

Analysis of a Leslie-Gower predator-prey model with Allee effect and fear effect

In this paper, the dynamical behaviors of a Leslie-Gower predator-prey model with Allee effect and fear effect are studied. First, we use Blow-Up method to explore the stability of the original point. Analyze the local stability of the non-negative equilibriums of the system. Taking the growth rate of predators as the Hopf bifurcation parameters. And give the condition of the model Hopf bifurcation. Using the method of calculating the first Lyapunov coefficient to discuss the direction of the Hopf bifurcation near the weak center.

math.DS↗

arXiv2023

Stability analysis of an SIR model with saturated infection rate and saturated treatment rate

Treatment rate has always been one of the most important factors affecting the spread of infectious diseases. In this paper, we study a treatment function SIR model with treatment rate related to the maximum treatment capacity, whose infection rate is also saturated nonlinear. By calculating and analyzing based on planar dynamic system, the existence and stability of disease-free equilibrium point of the model are found. And it is also found that the situation is more complex for the endemic equilibrium point of the model. Under the conditions of meeting different parameters, the number of endemic equilibrium points may be zero, one or two, and the behavior of the endemic equilibrium point may be a saddle point, a stable or unstable anti-saddle point or center, or even a degenerate case.

math.DS↗