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<p>This paper announces Hopf bifurcation and the application of a straightforward time-delayed feedback control (TDFC) method to multi-scroll chaotic Chua attractors, generated through parallel transformation. The paper provides the necessary and sufficient conditions for the existence of these attractors and establishes the critical Hopf bifurcation value at specific two-parameter control values (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1584_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>). Additionally, the study explores the effectiveness of the TDFC method in transitioning an initially unstable equilibrium point to a stable one. The application of TDFC demonstrates its ability to manage chaotic behaviors by stabilizing unstable equilibrium points, all while preserving the core structure of the system.</p>

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Analysis of Hopf bifurcation and time-delayed control in multi-scroll chaotic attractors produced by parallel transformation

  • 期刊论文

  • 发表日期：

    2025年1月25日

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  • Zaamoune Faiza,
  • Tidjani Menacer,
  • René Lozi

摘要

This paper announces Hopf bifurcation and the application of a straightforward time-delayed feedback control (TDFC) method to multi-scroll chaotic Chua attractors, generated through parallel transformation. The paper provides the necessary and sufficient conditions for the existence of these attractors and establishes the critical Hopf bifurcation value at specific two-parameter control values ( \(k\) k ). Additionally, the study explores the effectiveness of the TDFC method in transitioning an initially unstable equilibrium point to a stable one. The application of TDFC demonstrates its ability to manage chaotic behaviors by stabilizing unstable equilibrium points, all while preserving the core structure of the system.