Nonlinear Dynamics

, Volume 84, Issue 3, pp 1529–1539 | Cite as

Geometric analysis of a pest management model with Holling’s type III functional response and nonlinear state feedback control

  • Tongqian Zhang
  • Jian Zhang
  • Xinzhu Meng
  • Tonghua Zhang
Original Paper

Abstract

In this paper, based on a predator–prey model with Holling’s type III functional response, a pest management system with artificial interference is proposed. We assume that the artificial interference strategy will be taken to control pests when their number reaches a certain threshold. Based on this assumption, the artificial interference strategy of the system with nonlinear state feedback control is analyzed by using the geometric theory of ordinary differential equations. We first study the existence of periodic solutions of the model by successor functions and then the stability of periodic solutions. Finally, numerical simulations are given to illustrate our theoretic conclusions.

Keywords

Integrated pest management (IPM) Nonlinear state feedback control Holling’s type III functional response Saturation effect Periodic solution Stability 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Tongqian Zhang
    • 1
    • 2
  • Jian Zhang
    • 1
  • Xinzhu Meng
    • 1
    • 2
  • Tonghua Zhang
    • 3
  1. 1.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoPeople’s Republic of China
  2. 2.State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and TechnologyShandong University of Science and TechnologyQingdaoPeople’s Republic of China
  3. 3.Department of MathematicsSwinburne University of TechnologyMelbourneAustralia

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