Abstract and Applied Analysis

Geometric Analysis of an Integrated Pest Management Model Including Two State Impulses

Wencai Zhao, Yulin Liu, Tongqian Zhang, and Xinzhu Meng

Full-text: Open access

Abstract

According to integrated pest management strategies, we construct and investigate the dynamics of a Holling-Tanner predator-prey system with state dependent impulsive effects by releasing natural enemies and spraying pesticide at different thresholds. Applying the Dulacs criterion, the global stability of the positive equilibrium in the system without impulsive effect is discussed. By using impulsive differential equation geometry theory and the method of successor functions, we prove the existence of periodic solution of the system with state dependent impulsive effects. Furthermore, the stability conditions of periodic solutions are obtained. Some simulations are exerted to illustrate the feasibility of our main results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 963072, 18 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607549

Digital Object Identifier
doi:10.1155/2014/963072

Mathematical Reviews number (MathSciNet)
MR3186991

Zentralblatt MATH identifier
07023408

Citation

Zhao, Wencai; Liu, Yulin; Zhang, Tongqian; Meng, Xinzhu. Geometric Analysis of an Integrated Pest Management Model Including Two State Impulses. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 963072, 18 pages. doi:10.1155/2014/963072. https://projecteuclid.org/euclid.aaa/1412607549


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