Stability and Hopf bifurcation of a predator-prey model with Smith growth rate and Monod–Haldane functional response

This paper focuses on the qualitative analysis of the diffusive Monod–Haldane predator-prey model with Smith growth rate under Neumann boundary condition. First, the stability of the solution of corresponding ODE system is studied, and then the Hopf divergence direction and the stability of periodic...

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Bibliographic Details
Published in:Advances in continuous and discrete models Vol. 2025; no. 1; p. 46
Main Authors: Feng, Xiaozhou, Li, Kunyu, Liu, Mengyan, Wang, Lin, Wang, Tonghui
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2025
Springer Nature B.V
Subjects:
Analysis
Biomathematical Modelling and Stochastic Analysis
Boundary conditions
Centre manifold theory
Difference and Functional Equations
Diffusion coefficient
Diffusion rate
Divergence
Equilibrium
Functional Analysis
Growth models
Hopf bifurcation
Linear operators
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Predation
Predator-prey simulation
Predators
Qualitative analysis
Stability analysis
Hopf analysis
Neumann boundary condition
Smith growth rate
Turing instability
ISSN:1687-1839, 2731-4235, 1687-1847
Online Access:Get full text
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Summary:This paper focuses on the qualitative analysis of the diffusive Monod–Haldane predator-prey model with Smith growth rate under Neumann boundary condition. First, the stability of the solution of corresponding ODE system is studied, and then the Hopf divergence direction and the stability of periodic solutions are given. Then considering the non-uniform distribution of populations in nature, by standard linear operator theory and center manifold theorem, the Turing instability and the Hopf bifurcation of the PDE system with diffusion effects is analyzed. Finally, the theoretical calculation results are verified by numerical simulations. It can be observed that the variation of Smith growth rate and diffusion coefficient within a certain range can increase the complexity of the model.
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ISSN:1687-1839
2731-4235
1687-1847
DOI:10.1186/s13662-025-03912-0