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Dynamic complexity of microbial pesticide model

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Abstract

In this paper, a mathematical model for the entomopathogenic nematode attacking the pest is investigated. This novel theoretical framework could result in an objective criterion on how to release the entomopathogenic nematode in order to control the pest population under the economic threshold (ET) which indicates the maximally admissible pest densities. Firstly, continuous release of the entomopathogenic nematode is taken. By using qualitative analysis method, the sufficient condition of the global stability of the positive equilibria and the existence and uniqueness of limit cycle of the system are obtained. Secondly, impulsive release of the entomopathogenic nematode is also considered. Using the Floquet’s theorem and small-amplitude perturbation, we obtain that the pest-free periodic solution is locally stable if some conditions are satisfied. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations.

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Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Tieying Wang & Lansun Chen

  2. College of Science, Dalian Nationalities University, Dalian, 116605, People’s Republic of China

    Tieying Wang

Authors
  1. Tieying Wang
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  2. Lansun Chen
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Correspondence to Tieying Wang.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 10771179).

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Wang, T., Chen, L. Dynamic complexity of microbial pesticide model. Nonlinear Dyn 58, 539–552 (2009). https://doi.org/10.1007/s11071-009-9499-7

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  • DOI: https://doi.org/10.1007/s11071-009-9499-7

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