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Stabilization for a class of delay systems via Z-type control.
1Vanderbilt University, Electrical Engineering, 221 Kirkland Hall, Nashville, TN 37235, USA.
ISA Transactions
|October 1, 2022
Summary
This study introduces the Z-type control method to stabilize predator-prey populations, ensuring they reach target levels. The research explores both direct and indirect control strategies for time-delayed ecological models.
Area of Science:
- Ecology
- Control Theory
- Mathematical Biology
Background:
- Predator-prey models are fundamental in ecology.
- Time delays in population dynamics can lead to instability.
- Control methods are needed to manage species populations.
Purpose of the Study:
- To investigate the Z-type control method for stabilizing two-species predator-prey models.
- To design direct and indirect controllers for population stabilization.
- To analyze the impact of time delays on population dynamics and control.
Main Methods:
- Development of Z-type controllers for direct and indirect control scenarios.
- Theoretical justification of the Z-type control construction.
- Discretization of state-space systems using the Euler forward formula.
- Numerical simulations to validate controller performance.
Main Results:
- The Z-type control method effectively stabilizes predator-prey populations towards desired values.
- Non-linear activation functions can accelerate the control process.
- Discrete versions of controlled systems were derived and analyzed.
Conclusions:
- The Z-type control method is a viable strategy for managing time-delayed predator-prey systems.
- The study provides a framework for designing and implementing such controllers.
- Numerical simulations confirm the theoretical findings and controller efficacy.
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