Stability analysis and chaos control in a discrete predator-prey system with Allee effect, fear effect, and refuge

This paper investigates the complex dynamical behavior of a discrete prey-predator system with a fear factor, a strong Allee effect, and prey refuge. The existence and stability of fixed points in the system are discussed. By applying the central manifold theorem and bifurcation theory, we have esta...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 5; pp. 13462 - 13491
Main Authors Su, Xiaoming, Wang, Jiahui, Bao, Adiya
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
allee effect
chaos control
discrete prey-predator system
fear effect
flip bifurcation
neimark-sacker bifurcation
refuge
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Summary:This paper investigates the complex dynamical behavior of a discrete prey-predator system with a fear factor, a strong Allee effect, and prey refuge. The existence and stability of fixed points in the system are discussed. By applying the central manifold theorem and bifurcation theory, we have established the occurrence of various types of bifurcations, including flip bifurcation and Neimark-Sacker bifurcation. Furthermore, to address the observed chaotic behavior in the system, three controllers were designed by employing state feedback control, OGY feedback control, and hybrid control methods. These controllers serve to control chaos in the proposed system and identify specific conditions under which chaos or bifurcations can be stabilized. Finally, the theoretical analyses have been validated through numerical simulations.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024656