Stability and bifurcation analysis in a discrete-time logistic model under harvested and feedback control

Volume 36, Issue 3, pp 251--262 https://dx.doi.org/10.22436/jmcs.036.03.01

Publication Date: August 06, 2024 Submission Date: February 06, 2024 Revision Date: March 09, 2024 Accteptance Date: June 29, 2024

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Authors

A. Suryanto - Department of Mathematics‎, ‎Faculty of Mathematics and Natural Sciences, ‎University of Brawijaya, ‎Jl‎. ‎Veteran Malang 65145, ‎Indonesia. I. Darti - Department of Mathematics‎, ‎Faculty of Mathematics and Natural Sciences, ‎University of Brawijaya, ‎Jl‎. ‎Veteran Malang 65145, ‎Indonesia. Trisilowati - Department of Mathematics‎, ‎Faculty of Mathematics and Natural Sciences, ‎University of Brawijaya, ‎Jl‎. ‎Veteran Malang 65145, ‎Indonesia.

Abstract

We discuss a discrete-time logistic model with harvesting and feedback control‎. ‎The discrete model is obtained by applying Euler's method to its continuous model‎. ‎We first determine the equilibrium points‎, ‎including their existence conditions and their local stability properties‎. ‎We then apply the central manifold theorem and bifurcation theory to establish conditions for the existence of both period-doubling bifurcation and Neimark-Sacker bifurcation around the positive equilibrium point‎. ‎Finally‎, ‎we provide some numerical simulations to verify the feasibility of the theoretical results and demonstrate the complex dynamic behavior‎. ‎Moreover‎, ‎the presence of chaos in the system is justified numerically by the computed maximum Lyapunov exponent‎.

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Keywords

• Logistic model
• feedback control
• period-doubling bifurcation
• Neimark-Sacker bifurcation
• Lyapunov exponent
• chaotic behavior‎

MSC

•  37N25
•  39A30
•  39A60
•  92D25

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