On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy

Abstract

This paper introduces a novel fractional Ikeda-based memristor map and investigates its non-linear dynamics under commensurate and incommensurate orders using various numerical techniques, including Lyapunov exponent analysis, phase portraits, and bifurcation diagrams. The results reveal diverse and complex system behaviors arising from the interplay of different fractional orders in the proposed map. Furthermore, the study employs the sample entropy test to quantify complexity and validate the presence of chaos. Non-linear controllers are also presented to stabilize and synchronize the model. The research emphasizes the system’s sensitivity to the fractional order parameters, leading to distinct dynamic patterns and stability regimes. The memristor-based chaotic map exhibits rich and intricate behavior, making it an interesting and important area of research.

Keywords

• Ikeda-based memristor map
• discrete fractional calculus
• bifurcation
• chaotic dynamics
• sample entropy
• control