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Dynamics for a fractional-order predator-prey model with group defense
1Business school, Jiangsu University of Technology, Changzhou, 213001, P.R. China. Regales1988@sina.com.
Scientific Reports
|March 19, 2020
Summary
This study introduces a new fractional order predator-prey model incorporating group defense. Mathematical analysis confirms the model
Area of Science:
- Mathematical Biology
- Dynamical Systems Theory
- Fractional Calculus
Background:
- Predator-prey models are fundamental in ecology for understanding population dynamics.
- Incorporating group defense mechanisms offers a more realistic portrayal of ecological interactions.
- Fractional order differential equations provide a more nuanced approach to modeling complex biological systems.
Purpose of the Study:
- To develop and analyze a novel fractional order predator-prey model that includes the concept of group defense.
- To investigate the fundamental dynamical properties of this new model, including solution behavior and stability.
- To explore the potential for oscillatory dynamics through the analysis of Hopf bifurcations.
Main Methods:
- Application of Lipschitz condition and inequality techniques to establish the existence, uniqueness, and boundedness of solutions.
- Utilizing basic mathematical analysis and linearization approaches to determine the stability of equilibrium points.
- Employing fractional order differential equation theory, specifically Hopf bifurcation theory, to analyze oscillatory behaviors.
Main Results:
- Sufficient conditions were derived for the existence, uniqueness, and boundedness of the model's solutions.
- Criteria for the local asymptotic stability of equilibrium points were established.
- The existence of Hopf bifurcations was confirmed, indicating potential for complex population dynamics.
Conclusions:
- The developed fractional order predator-prey model with group defense exhibits well-defined dynamical properties.
- The analysis provides a theoretical foundation for understanding population dynamics influenced by group defense strategies.
- Simulation results support the theoretical findings, validating the model's behavior.
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