Catastrophe control of aphid populations model

Lichun Zhao; Jingna Liu; Bing Liu; Yuan Li; Huiyan Zhao; Lichun Zhao; Jingna Liu; Bing Liu; Yuan Li; Huiyan Zhao

doi:10.3934/mbe.2022336

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 7122-7137. doi: 10.3934/mbe.2022336

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Research article Special Issues

Catastrophe control of aphid populations model

1.
School of Mathematics and Information Science, Anshan Normal University, Ashan 114007, China
2.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
3.
State Key Laboratory of Crop Stress Biology in Arid Areas, School of Plant Protection, Northwest A and F University, Yangling 712100, China

Received: 08 February 2022 Revised: 28 March 2022 Accepted: 18 April 2022 Published: 13 May 2022

Considering the effect of the natural enemy on aphid populations, the corresponding model with delay is built. The model is analyzed using the qualitative theory of differential equations and catastrophe theory etc. For the outbreak phenomenon of aphid populations, the corresponding management model is proposed and the catastrophe controller is designed to keep the system in a virtuous cycle by means of the qualitative theory of impulsive differential equations. In the mean time, some simulations are carried to prove the results. The paper not only provides a new method for catastrophe control but also expands the application fields of catastrophe control.

Keywords:

catastrophe theory,
aphid populations,
catastrophe control,
delay effect,
the qualitative theory of impulsive differential equations

Citation: Lichun Zhao, Jingna Liu, Bing Liu, Yuan Li, Huiyan Zhao. Catastrophe control of aphid populations model[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 7122-7137. doi: 10.3934/mbe.2022336

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Abstract

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