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Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior
Rohisha Tuladhar1, Fidel Santamaria1, Ivanka Stamova2
1Department of Biology, University of Texas at San Antonio, San Antonio, TX 78249, USA.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study introduces a fractional-order cooperation model for n-species, incorporating delays and impulsive control. The research extends stability analysis to fractional calculus, offering new insights into ecological dynamics.
Area of Science:
- Mathematical Biology
- Ecology
- Dynamical Systems
Background:
- Lotka-Volterra models are fundamental in population dynamics.
- Delayed differential equations capture ecological memory effects.
- Fractional calculus offers a more nuanced approach to modeling complex systems.
Purpose of the Study:
- To develop and analyze a fractional-order n-species Lotka-Volterra cooperation model with delays.
- To investigate the impact of impulsive control on system stability.
- To extend existing stability theory to fractional dynamical systems.
Main Methods:
- Utilizing Caputo fractional derivatives for model formulation.
- Applying impulsive control strategies to analyze stability.
- Investigating Mittag-Leffler stability, practical stability, and stability with respect to sets.
Main Results:
- Demonstrated the application of impulsive control to fractional-order delayed Lotka-Volterra models.
- Extended stability criteria from integer-order to fractional-order systems.
- Provided a framework for analyzing stability in complex ecological models.
Conclusions:
- Fractional-order dynamics and impulsive control are crucial for understanding n-species cooperation.
- The study bridges the gap between integer-order and fractional-order ecological modeling.
- This work offers a foundation for further research in fractional ecological systems.
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