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Analysis of a predator-prey system with predator switching
Q J A Khan1, E Balakrishnan, G C Wake
1Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, PO Box 36, Postal Code 123, Al-Khod, Oman.
Bulletin of Mathematical Biology
|December 13, 2003
Summary
This study models predator-prey dynamics with prey group defense. Increased environmental resources (carrying capacity) can paradoxically lead to predator extinction, supporting the "paradox of enrichment".
Area of Science:
- Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Predator-prey interactions are fundamental in ecology.
- Prey group defense is a known survival strategy.
- The 'paradox of enrichment' suggests increased resources can destabilize ecosystems.
Purpose of the Study:
- To investigate predator-prey dynamics incorporating prey group defense.
- To analyze the impact of environmental enrichment on population stability.
- To examine the conditions leading to predator extinction.
Main Methods:
- Development of a system of ordinary differential equations.
- Analysis of thresholds, equilibria, and stability.
- Bifurcation analysis using carrying capacity as a parameter.
Main Results:
- The model identifies critical thresholds and stable equilibria for the predator-prey system.
- A Hopf bifurcation was observed, indicating potential for oscillations.
- Sufficiently high carrying capacity predicts predator extinction.
Conclusions:
- Prey group defense can alter predator-prey dynamics.
- Environmental enrichment, while seemingly beneficial, can destabilize predator populations.
- The findings provide mathematical support for the 'paradox of enrichment' in ecological models.