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<p>Multi-wing hyperchaotic systems with large Lyapunov exponents and controllable topological structures are more useful in practical applications. This paper proposes a novel four-dimensional hyperchaotic system that generates multi-wing attractors through a hierarchical harmonic modulation mechanism. A nonlinear hierarchical harmonic modulation controller is designed to generate multi-wing attractors with adjustable wing counts by varying the number and distribution of equilibrium points. The proposed system exhibits robust hyperchaotic characteristics with two positive Lyapunov exponents, and the largest Lyapunov exponent is substantially elevated due to the enhanced nonlinearity and additional dimension introduced by the modulation mechanism. Furthermore, the integer-order system is extended to the fractional-order domain using the Caputo derivative. The 0-1 test confirms that the system exhibits strong chaotic behavior down to a fractional order of 0.88. Complexity analysis reveals that the Spectral Entropy of the proposed system significantly outperforms the original system. Finally, a DSP hardware implementation successfully captures the multi-wing hyperchaotic attractors, validating the scientific soundness and practical feasibility of the proposed model.</p>

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Design and DSP implementation of a 4D fractional-order multi-wing hyperchaotic system based on hierarchical harmonic modulation

  • 期刊论文

  • 发表日期：

    2026年5月1日

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  • Lixin Diao,
  • Guodong Li,
  • Liang Xue,
  • Wenjie Li

摘要

Multi-wing hyperchaotic systems with large Lyapunov exponents and controllable topological structures are more useful in practical applications. This paper proposes a novel four-dimensional hyperchaotic system that generates multi-wing attractors through a hierarchical harmonic modulation mechanism. A nonlinear hierarchical harmonic modulation controller is designed to generate multi-wing attractors with adjustable wing counts by varying the number and distribution of equilibrium points. The proposed system exhibits robust hyperchaotic characteristics with two positive Lyapunov exponents, and the largest Lyapunov exponent is substantially elevated due to the enhanced nonlinearity and additional dimension introduced by the modulation mechanism. Furthermore, the integer-order system is extended to the fractional-order domain using the Caputo derivative. The 0-1 test confirms that the system exhibits strong chaotic behavior down to a fractional order of 0.88. Complexity analysis reveals that the Spectral Entropy of the proposed system significantly outperforms the original system. Finally, a DSP hardware implementation successfully captures the multi-wing hyperchaotic attractors, validating the scientific soundness and practical feasibility of the proposed model.