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<p>This study investigates the nonlinear characteristics of high-dimensional complex dynamical systems and develops an extended Melnikov method tailored for fractional-order systems. By treating the fractional-order derivative term as the perturbation term, the chaos threshold is quantitatively calculated based on this criterion. The effectiveness of the proposed criteria is verified through phase diagram, time series diagram and local lyapunov exponent diagram. On the theoretical side, the explicit analytical expression of the fractional-order Melnikov function is derived. The proposed framework establishes a robust theoretical basis for chaos identification and quantitative analysis in high-dimensional fractional-order systems, especially Duffing-type systems.</p>

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Chaos analysis of high-dimensional fractional-order nonlinear systems: the extended Melnikov method

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Jiale Zhang,
  • Jiaquan Xie,
  • Wei Shi,
  • Jianguo Liang,
  • Mingxu Yi,
  • Yan Cui,
  • Yifen Li

摘要

This study investigates the nonlinear characteristics of high-dimensional complex dynamical systems and develops an extended Melnikov method tailored for fractional-order systems. By treating the fractional-order derivative term as the perturbation term, the chaos threshold is quantitatively calculated based on this criterion. The effectiveness of the proposed criteria is verified through phase diagram, time series diagram and local lyapunov exponent diagram. On the theoretical side, the explicit analytical expression of the fractional-order Melnikov function is derived. The proposed framework establishes a robust theoretical basis for chaos identification and quantitative analysis in high-dimensional fractional-order systems, especially Duffing-type systems.