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<p>In this work, we use the fourth-order averaging theory to investigate the existence of limit cycles bifurcating from a zero–Hopf equilibrium for general polynomial differential systems in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40863_2025_489_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> with cubic homogeneous non-linearities. The result indicates there are at most 10 limit cycles that can bifurcate from this zero–Hopf equilibrium.</p>

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3-Dimensional zero–Hopf bifurcation via averaging theory of fourth order

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • Achref Eddine Tabet,
  • Amar Makhlouf,
  • Sara Kassa

摘要

In this work, we use the fourth-order averaging theory to investigate the existence of limit cycles bifurcating from a zero–Hopf equilibrium for general polynomial differential systems in \(\mathbb {R}^3\) R 3 with cubic homogeneous non-linearities. The result indicates there are at most 10 limit cycles that can bifurcate from this zero–Hopf equilibrium.