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The current research introduces a 3D sine-based memristor map with fractional order, developed by extending a two-dimensional sine map through the combination of a discrete memristor. A comprehensive investigation of its nonlinear dynamics was carried out under both commensurate and incommensurate fractional derivatives, utilizing a selection of numerical techniques such as Lyapunov exponent analysis, phase portrait visualization, and bifurcation diagram plotting. The findings highlight the map’s high sensitivity to changes in both system and fractional-order parameters, causing the onset of a wide variety of dynamic behaviors. Additionally, complexity was quantitatively assessed using sample entropy (SampEn) and \(C_0\) complexity metrics, while the occurrence of chaotic dynamics was confirmed via the 0–1 test. All theoretical results were validated through MATLAB-based simulations.

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The Chaotic Fractional Sine-Based Memristor Map: Dynamical Analysis and Numerical Simulations

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  • 发表日期：

    2026年

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  • Imane Zouak,
  • Adel Ouannas,
  • Abderrahmane Abbes

摘要

The current research introduces a 3D sine-based memristor map with fractional order, developed by extending a two-dimensional sine map through the combination of a discrete memristor. A comprehensive investigation of its nonlinear dynamics was carried out under both commensurate and incommensurate fractional derivatives, utilizing a selection of numerical techniques such as Lyapunov exponent analysis, phase portrait visualization, and bifurcation diagram plotting. The findings highlight the map’s high sensitivity to changes in both system and fractional-order parameters, causing the onset of a wide variety of dynamic behaviors. Additionally, complexity was quantitatively assessed using sample entropy (SampEn) and \(C_0\) complexity metrics, while the occurrence of chaotic dynamics was confirmed via the 0–1 test. All theoretical results were validated through MATLAB-based simulations.