Threshold control strategy for a Filippov model with group defense of pests and a constant-rate release of natural enemies

Baolin Kang; Xiang Hou; Bing Liu; Baolin Kang; Xiang Hou; Bing Liu

doi:10.3934/mbe.2023537

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12076-12092. doi: 10.3934/mbe.2023537

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Threshold control strategy for a Filippov model with group defense of pests and a constant-rate release of natural enemies

1.
College of Mathematics and Information Science, Anshan Normal University, Anshan 114007, China
2.
Research Center for Theoretical Ecology, School of Geography and Environment, Jiangxi Normal University, Nanchang 330022, China

Academic Editor: Yan Liu

Received: 29 January 2023 Revised: 27 March 2023 Accepted: 17 April 2023 Published: 15 May 2023

In this paper, we establish an integrated pest management Filippov model with group defense of pests and a constant rate release of natural enemies. First, the dynamics of the subsystems in the Filippov system are analyzed. Second, the dynamics of the sliding mode system and the types of equilibria of the Filippov system are discussed. Then the complex dynamics of the Filippov system are investigated by using numerical analysis when there is a globally asymptotically stable limit cycle and a globally asymptotically stable equilibrium in two subsystems, respectively. Furthermore, we analyze the existence region of a sliding mode and pseudo equilibrium, as well as the complex dynamics of the Filippov system, such as boundary equilibrium bifurcation, the grazing bifurcation, the buckling bifurcation and the crossing bifurcation. These complex sliding bifurcations reveal that the selection of key parameters can control the population density no more than the economic threshold, so as to prevent the outbreak of pests.
- Filippov system,
- sliding mode,
- equilibrium,
- sliding bifurcation,
- group defense
Citation: Baolin Kang, Xiang Hou, Bing Liu. Threshold control strategy for a Filippov model with group defense of pests and a constant-rate release of natural enemies[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12076-12092. doi: 10.3934/mbe.2023537

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Abstract

In this paper, we establish an integrated pest management Filippov model with group defense of pests and a constant rate release of natural enemies. First, the dynamics of the subsystems in the Filippov system are analyzed. Second, the dynamics of the sliding mode system and the types of equilibria of the Filippov system are discussed. Then the complex dynamics of the Filippov system are investigated by using numerical analysis when there is a globally asymptotically stable limit cycle and a globally asymptotically stable equilibrium in two subsystems, respectively. Furthermore, we analyze the existence region of a sliding mode and pseudo equilibrium, as well as the complex dynamics of the Filippov system, such as boundary equilibrium bifurcation, the grazing bifurcation, the buckling bifurcation and the crossing bifurcation. These complex sliding bifurcations reveal that the selection of key parameters can control the population density no more than the economic threshold, so as to prevent the outbreak of pests.

References

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