Integrated Pest Management System with Impulsive Control of Spatial Heterogeneity

Hongling Zhou; Lin Shen; Shu Wang

doi:10.4208/jpde.v35.n1.3

Authors

Hongling Zhou School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China
Lin Shen School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China
Shu Wang College of Applied Science, Beijing University of Technology, Beijing 100124, China

DOI:

https://doi.org/10.4208/jpde.v35.n1.3

Keywords:

Integrated pest management, eigenvalue problem, pest control, diffusion.

Abstract

An impulsive integrated pest management system with diffusion is investigated within this paper. The conditions for pest eradication of the impulsive system without natural enemies are established based on the Krein-Rutman theorem and the comparison principle for parabolic equations. Integrated pest management can be achieved at an exponential rate, when the principal eigenvalues of the auxiliary system is large enough. Numerical simulations are presented to demonstrate the theoretical results. A discussion is given at the end.