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Bifurcation analysis of a reaction-diffusion-advection predator-prey system with delay
Honghua Bin1, Daifeng Duan2, Junjie Wei1,2
1Department of Mathematics, Jimei University, Jimei, Fujian 361021, China.
Mathematical Biosciences and Engineering : MBE
|July 28, 2023
Summary
This study examines a predator-prey model with time delays, revealing Hopf bifurcation. Simulations show how time delays and advection impact system dynamics.
Area of Science:
- Mathematical Biology
- Theoretical Ecology
- Dynamical Systems
Background:
- Predator-prey models are fundamental in ecology.
- Advection and time delays introduce complex dynamics.
- Understanding these factors is crucial for ecological stability.
Purpose of the Study:
- To analyze a diffusive predator-prey system incorporating advection and time delay.
- To investigate the occurrence of Hopf bifurcation as a function of conversion delay.
- To develop a method for determining Hopf bifurcation direction and stability.
Main Methods:
- Utilizing a reaction-diffusion model.
- Applying an improved center manifold reduction method.
- Employing normal form theory for bifurcation analysis.
Main Results:
- Hopf bifurcation is identified as a key phenomenon.
- The conversion delay ($ \tau $) acts as a bifurcation parameter.
- Simulations demonstrate the influence of time delay ($ \tau $) and advection ($ \alpha $) on system behavior.
Conclusions:
- The conversion delay significantly influences the system's stability.
- Advection plays a critical role in shaping population dynamics.
- The developed methods provide insights into complex ecological models.
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