Density-dependent integrated pest management model with instantaneous and non-instantaneous impulsive effects

In integrated pest management (IPM), the coordination of chemical and biological approaches is crucial for achieving ecologically sustainable pest control. This paper proposes a model that integrates density-dependent mechanisms with both instantaneous and non-instantaneous impulsive effects. The model examines the application of “targeted pesticides” designed to specifically impact pest populations, while incorporating dynamic release strategies based on the densities of natural enemy populations. Additionally, it accounts for the decay of pesticide residues over time, as well as the dynamics of predation and conversion rates by natural enemies. Utilizing impulsive differential equations, comparison theorems, and Floquet theory, we derive sufficient conditions for the global asymptotic stability of the periodic solution for pest eradication and analyze the boundedness and permanence of the system. Numerical simulations reveal complex dynamics of the model, including period-doubling bifurcation, chaos, period-halving bifurcation, and the coexistence of multiple attractors, as well as the impact of key parameters on the threshold of pest eradication. Furthermore, we perform a numerical analysis of a density-dependent state feedback IPM model. The results show that the frequency of pesticide application can be dynamically adjusted in combination with the release of natural enemies. The overall strategy design based on different numerical ranges of each parameter is conducive to improving the control efficiency and reducing the risk of pesticide use.