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

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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.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Tongqian Zhang, Jian Zhang & Xinzhu Meng

  2. State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Tongqian Zhang & Xinzhu Meng

  3. Department of Mathematics, Swinburne University of Technology, Melbourne, VIC, 3122, Australia

    Tonghua Zhang

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  1. Tongqian Zhang
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  2. Jian Zhang
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Correspondence to Tongqian Zhang.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 11371230), Shandong Provincial Natural Science Foundation, China (No. ZR2012AM012, No. ZR2015AQ001), a Project for Higher Educational Science and Technology Program of Shandong Province of China (No. J13LI05), Joint Innovative Center for Safe and Effective Mining Technology and Equipment of Coal Resources, Shandong Province of China and SDUST Research Fund (2014TDJH102).

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Zhang, T., Zhang, J., Meng, X. et al. Geometric analysis of a pest management model with Holling’s type III functional response and nonlinear state feedback control. Nonlinear Dyn 84, 1529–1539 (2016). https://doi.org/10.1007/s11071-015-2586-z

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  • DOI: https://doi.org/10.1007/s11071-015-2586-z

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