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Dynamical analysis of a discrete two-patch model with the Allee effect and nonlinear dispersal
Minjuan Gao1, Lijuan Chen1, Fengde Chen1
1School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, Fujian, China.
Mathematical Biosciences and Engineering : MBE
|June 14, 2024
Summary
This study analyzes a two-patch population model with Allee effect and nonlinear dispersal. We explore how these factors influence population dynamics and stability in connected habitats.
Area of Science:
- Mathematical Biology
- Ecology
- Population Dynamics
Background:
- Population models are crucial for understanding species survival.
- The Allee effect and nonlinear dispersal significantly impact population dynamics.
Purpose of the Study:
- To investigate the dynamic behavior of a discrete-time two-patch model.
- To analyze the influence of the Allee effect and nonlinear dispersal on system dynamics.
Main Methods:
- Analysis of fixed points and their stability.
- Application of central manifold theorem and bifurcation theory.
- Numerical simulations to validate theoretical findings.
Main Results:
- Existence and stability of fixed points were determined.
- Fold and flip bifurcations were identified and analyzed.
- The Allee effect and nonlinear dispersal were shown to alter system dynamics.
Conclusions:
- The study provides insights into the complex dynamics of spatially structured populations.
- Understanding these dynamics is vital for conservation and management strategies.
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