Complex dynamics of a nonlinear impulsive control predator-prey model with Leslie-Gower and B-D functional response

A good pulse control strategy should depend on the numbers of pests and natural enemies as determined via an integrated pest control strategy. Taking this into consideration, here, a nonlinear impulsive predator-prey model with improved Leslie-Gower and Beddington-DeAngelis functional response terms...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 6; pp. 14454 - 14472
Main Authors Li, Changtong, Cheng, Dandan, Feng, Xiaozhou, Liu, Mengyan
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
bifurcation
global asymptotic stability
nonlinear impulsive
numerical simulation
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Summary:A good pulse control strategy should depend on the numbers of pests and natural enemies as determined via an integrated pest control strategy. Taking this into consideration, here, a nonlinear impulsive predator-prey model with improved Leslie-Gower and Beddington-DeAngelis functional response terms is qualitatively analyzed. The existence of a periodic solution for pest eradication has been obtained and the critical condition of global asymptotic stability has been established by using the impulsive differential equation Floquet theory. Furthermore, the conditions for the lasting survival of the system has been proved by applying a comparison theorem for differential equations. Additionally, a stable positive periodic solution has been obtained by applying bifurcation theory. To understand how nonlinear pulses affect the dynamic behavior of a system, MATLAB was used to conduct numerical simulations to show that the model has very complex dynamical behavior.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024702