Exploration on dynamics in a discrete predator-prey competitive model involving feedback controls

Area of Science:

• Mathematical Biology
• Ecology
• Dynamical Systems

Background:

• Predator-prey models are crucial for understanding ecological dynamics.
• Time-varying delays and feedback controls introduce complex behaviors in ecological systems.
• Discrete models offer a framework for analyzing population dynamics over time intervals.

Purpose of the Study:

• To develop a new discrete predator-prey competitive model incorporating time-varying delays and feedback controls.
• To derive conditions ensuring the permanence of the established model.
• To investigate the existence and global attractiveness of periodic solutions.

Main Methods:

• Utilizing difference inequality knowledge to establish permanence conditions.
• Applying mathematical analysis to prove the existence and global attractiveness of periodic solutions.
• Employing computer simulations for verification of theoretical results.

Main Results:

• A sufficient condition for the permanence of the discrete predator-prey competitive model with time-varying delays and feedback controls was derived.
• Under specific parameter conditions, the existence and global attractiveness of the periodic solution (without delay) were proven.
• Numerical simulations confirmed the theoretical findings.

Conclusions:

• The study successfully established a new discrete predator-prey model with complex dynamics.
• The derived conditions provide theoretical guarantees for population persistence.
• The findings offer novel insights and complement existing knowledge in ecological modeling.