Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control

Area of Science:

• Ecology
• Mathematical Biology
• Integrated Pest Management

Background:

• Traditional integrated pest management (IPM) models are enhanced by incorporating realistic factors such as limited resources, predator-prey interactions, and agricultural insect monitoring data.
• Biotechnology advancements enable more sophisticated IPM models that consider complex ecological dynamics.

Purpose of the Study:

• To propose and analyze a nonlinear, state-dependent feedback control model for pest-natural enemy integrated management.
• To investigate the dynamical behavior and stability of the proposed pest management system under various conditions.

Main Methods:

• Development of a nonlinear pest-natural enemy integrated management system model.
• Inclusion of anti-predator behavior, density-dependent pest killing rates, and natural enemy release amounts.
• Analysis of impulsive and phase sets, derivation of the Poincaré map, and investigation of periodic solutions (order-1 and order-k).

Main Results:

• The study provides an analytic expression for the Poincaré map.
• Existence, uniqueness, and global stability of order-1 periodic solutions are analyzed.
• The existence of higher-order periodic solutions (k≥2) is also discussed.

Conclusions:

• Theoretical analyses reveal the relationship between economic thresholds and key pest control factors.
• The research demonstrates complex dynamical behaviors arising from nonlinear impulsive control strategies in IPM.
• Findings contribute to a deeper understanding of advanced pest management system dynamics.