Bifurcation analysis and chaos control in a discrete epidemic system
type: Item
instance of: scholarly article
title: Bifurcation analysis and chaos control in a discrete epidemic system
zbMATH Open document ID: 1418.92195
DOI: 10.1155/2015/974868
author: Wei Tan
author: Jianguo Gao
author: Wenjun Fan
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: The dynamics of discrete \textit{SI} epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior \(\mathbb R_+^2\), the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system \(x \rightarrow x + \delta [r N(1 - N / K) - \beta \left(x y / N\right) -(\mu + m) x]\), \(y \rightarrow y + \delta [\beta \left(x y / N\right) -(\mu + d) y]\). Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 7025570
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/974868
OpenAlex ID: W1648391249
Wikidata QID: Q59105604
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description: scientific article; zbMATH DE number 7025570