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Bifurcation analysis for a single population model with advection.
Hua Zhang1, Junjie Wei2,3
1Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong, 264209, People's Republic of China.
Journal of Mathematical Biology
|October 28, 2022
Summary
This study explores population dynamics in advective environments, revealing that increased advection or death rates reduce population density. It also identifies conditions for Hopf bifurcations in ecological models.
Area of Science:
- Mathematical Biology
- Population Dynamics
- Theoretical Ecology
Background:
- Investigates single population models with general growth functions in advective environments.
- Examines the influence of advection and delay on population dynamics.
- Builds upon existing ecological models like Nicholson's blowflies and Mackey-Glass.
Purpose of the Study:
- To analyze the dynamics of population models in advective environments.
- To determine conditions for the existence of nonconstant positive steady states and Hopf bifurcations.
- To apply theoretical findings to specific models and explore numerical simulations.
Main Methods:
- Theoretical analysis of population dynamics equations.
- Investigation of steady states and stability analysis.
- Numerical simulations to observe population density changes and bifurcation phenomena.
Main Results:
- Established the existence of a nonconstant positive steady state.
- Provided sufficient conditions for Hopf bifurcation at the positive steady state.
- Demonstrated numerically that population density decreases with increased advection or death rates.
- Showed that delay-induced Hopf bifurcations are more likely with low advection or mortality.
Conclusions:
- Advection and death rates significantly impact population density.
- Hopf bifurcations are sensitive to advection, death rates, and time delays.
- The study provides insights into the complex dynamics of populations in challenging environments.
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