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Updated: Jan 7, 2026
20:36
Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
9.1K
Application of a class of difference equations in population dynamics
Changtong Li1, Jia Tian1, Mengxuan Ma2
1School of Science, Xi'an Technological University, No. 2 Xuefuzhonglu Road, Weiyang District, Xi'an, Shaanxi 710021, People's Republic of China.
Chaos (Woodbury, N.Y.)
|January 5, 2026
Summary
This study analyzes a discrete predator-prey model, revealing complex dynamics and bifurcations. Numerical simulations confirm theoretical findings on stability and Neimark-Sacker bifurcations in biological systems.
Area of Science:
- Mathematical Biology
- Ecology
- Dynamical Systems
Background:
- Discrete mathematical models are crucial for understanding complex biological systems.
- Predator-prey dynamics are fundamental in ecological studies.
- Nonlinear harvesting and functional responses introduce intricate behaviors.
Purpose of the Study:
- To investigate the stability and bifurcation dynamics of a discrete predator-prey model.
- To analyze a model incorporating Holling-II functional response and Michaelis-Menten harvesting.
- To identify conditions for transcritical and Neimark-Sacker bifurcations.
Main Methods:
- Semi-discretization method to derive the discrete system.
- Analysis of fixed point existence and local stability.
- Application of center manifold theorem and bifurcation theory.
Main Results:
- Determined transcritical bifurcation conditions at boundary fixed points (E1, E2, E3).
- Identified Neimark-Sacker bifurcation conditions at the positive fixed point (E4).
- Numerical simulations validated theoretical analyses and demonstrated complex dynamics.
Conclusions:
- The discrete predator-prey model exhibits rich dynamical behaviors, including bifurcations.
- Theoretical predictions of stability transitions and Neimark-Sacker bifurcations are supported by simulations.
- This research contributes to understanding complex dynamics in discrete biological systems.
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