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<p>This paper provides a rigorous proof of the existence of an attracting invariant torus in the phase portrait of the Muthuswamy–Chua–Ginoux system, a model of an electrical circuit with a single memristor governed by a nonlinear system of ordinary differential equations depending on eight real parameters. The result is established by proving that a fixed point of the corresponding Poincaré map undergoes a Neimark–Sacker bifurcation, giving rise to an invariant closed curve. The entire analysis is based on a Melnikov–type function. To conclude, numerical simulations are presented to illustrate the theoretical findings and corroborate the analytical results.</p>

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Invariant Torus in the Phase Portrait of the Muthuswamy–Chua–Ginoux System

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月29日

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  • Denis de Carvalho Braga,
  • Bráulio Augusto Garcia

摘要

This paper provides a rigorous proof of the existence of an attracting invariant torus in the phase portrait of the Muthuswamy–Chua–Ginoux system, a model of an electrical circuit with a single memristor governed by a nonlinear system of ordinary differential equations depending on eight real parameters. The result is established by proving that a fixed point of the corresponding Poincaré map undergoes a Neimark–Sacker bifurcation, giving rise to an invariant closed curve. The entire analysis is based on a Melnikov–type function. To conclude, numerical simulations are presented to illustrate the theoretical findings and corroborate the analytical results.