Realistic threshold policy with hysteresis to control predator-prey continuous dynamics

Area of Science:

• Ecology
• Mathematical Biology
• Systems Biology

Background:

• Predator-prey models are fundamental to understanding ecological dynamics.
• Classical models like Lotka-Volterra and Rosenzweig-MacArthur often predict species extinction.
• Density-dependent and ratio-dependent models are used to explore complex ecological interactions.

Purpose of the Study:

• To introduce a novel control policy, threshold policy with hysteresis (TPH), for predator-prey systems.
• To demonstrate TPH's ability to prevent species extinction in various ecological models.
• To provide a simple and intuitive method for designing TPH using virtual equilibrium points.

Main Methods:

• Application of the threshold policy with hysteresis (TPH) to Lotka-Volterra, Rosenzweig-MacArthur, and Arditi-Ginzburg models.
• Analysis of system dynamics under TPH to achieve bounded oscillations.
• Design of the TPH policy through the selection of virtual equilibrium points.

Main Results:

• The TPH policy successfully modifies system dynamics to ensure bounded oscillations.
• Extinction of either predator or prey species is avoided within the controlled region.
• The policy offers a straightforward design approach via virtual equilibrium points.

Conclusions:

• The threshold policy with hysteresis (TPH) is an effective control strategy for predator-prey models.
• TPH ensures ecological stability by preventing species extinction.
• The proposed method provides an intuitive and practical approach to ecological control system design.