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Nonlinear Dynamics

, Volume 93, Issue 2, pp 705–720 | Cite as

Dynamical analysis of a pest management Leslie–Gower model with ratio-dependent functional response

  • Jing Xu
  • Yuan Tian
  • Hongjian Guo
  • Xinyu Song
Original Paper

Abstract

Agricultural pests are great threat for agricultural production, and the development of effective pest control methods is becoming an interesting topic and attracts great attentions. In this work, an integrated pest management model with Leslie–Gower type and ratio-dependent functional response is investigated, and the sufficient conditions for the existence and stability of the order-1 periodic solution are obtained by applying successor function method and analogue of Poincaré criterion. Meanwhile, a cost minimization model by means of the order-1 periodic solution is formulated to determine the optimal control level. The theoretical results are verified by computer simulations for two specified models, and it indicates that the proposed control strategy could keep the pest below the economic level. In addition, to verify the complex dynamics of the proposed model, an order-2 periodic solution and an order-3 periodic solution are obtained by adjusting one key control parameter in the simulations.

Keywords

Integrated pest management Leslie–Gower model Periodic solution Ratio-dependent Stability 

Notes

Acknowledgements

This work is supposed by the National Natural Science Foundation of China (Nos.: 11671346, 11371306, 11401068), the Project for Science and Technology Open Cooperation of Henan Province (172106000071) and Nanhu Scholars Program of XYNU.

Compliance with ethical standards

Conflict of interests

The authors declare that there is no conflict of interests.

Supplementary material

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXinyang Normal UniversityXinyangChina
  2. 2.School of Information EngineeringDalian UniversityDalianChina

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