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This chapter applies the \(\psi _i\) -th Caputo-like operator to study a new fractional discrete memristive model with incommensurate orders. To illustrate their influence on the dynamics of the system, bifurcation, phase portraits, and the calculation of the maximum Lyapunov Exponent \((\textbf{LE}_{max})\) are employed. Additionally, to measure complexity and confirm chaos in the incommensurate system, we use the 0-1 test, \(C_{0}\) complexity, and the sample entropy approach (SampEn). Research suggests that the discrete memristive system with incommensurate fractional orders exhibits a variety of dynamical behaviors that are impacted by the incommensurate derivative values, such as hidden chaos, symmetry, and asymmetry attractors. MATLAB R2024a programs are used to obtain numerical simulations that deliver the work outcomes.

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On Incommensurate Fractional Chaotic Discrete Memristive Model: Chaos and Complexity

  • 章节

  • 发表日期：

    2026年

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  • Louiza Diabi,
  • Adel Ouannas,
  • Omar Kahouli

摘要

This chapter applies the \(\psi _i\) -th Caputo-like operator to study a new fractional discrete memristive model with incommensurate orders. To illustrate their influence on the dynamics of the system, bifurcation, phase portraits, and the calculation of the maximum Lyapunov Exponent \((\textbf{LE}_{max})\) are employed. Additionally, to measure complexity and confirm chaos in the incommensurate system, we use the 0-1 test, \(C_{0}\) complexity, and the sample entropy approach (SampEn). Research suggests that the discrete memristive system with incommensurate fractional orders exhibits a variety of dynamical behaviors that are impacted by the incommensurate derivative values, such as hidden chaos, symmetry, and asymmetry attractors. MATLAB R2024a programs are used to obtain numerical simulations that deliver the work outcomes.