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Discrete Memristor and Discrete Memristive Systems.

Shaobo He1, Donglin Zhan1, Huihai Wang1

  • 1School of Physics and Electronics, Central South University, Changsha 410083, China.

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Summary
This summary is machine-generated.

This study introduces mathematical models for discrete memristors using fractional calculus. Researchers found that hysteresis area decreases with higher input frequency and lower derivative order, demonstrating potential engineering applications.

Keywords:
digital circuitsdiscrete modeling of memristorfractional-order differencememristive systemmemristor

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Area of Science:

  • Nonlinear Dynamics
  • Fractional Calculus
  • Solid-State Physics

Background:

  • Memristors are fundamental electronic components with memory properties.
  • Discrete memristor models are crucial for digital circuit design.
  • Fractional calculus offers advanced modeling capabilities for complex systems.

Purpose of the Study:

  • To develop and analyze discrete memristor models using Caputo and G-L fractional differences.
  • To investigate the impact of frequency and derivative order on memristor hysteresis.
  • To design and implement fractional-order discrete memristive systems and circuits.

Main Methods:

  • Mathematical modeling of discrete memristors using Caputo and G-L fractional differences.
  • Numerical analysis of hysteresis loops and memory effects.
  • Introduction of fractional-order discrete memristors into the Sine map to create new systems.
  • FPGA implementation for hardware validation.

Main Results:

  • Observed "∞"-type hysteresis loops with bipolar periodic input.
  • Hysteresis area inversely correlates with input signal frequency and derivative order.
  • Chaos and controllable complexity were found in the designed discrete memristive systems.
  • Successful FPGA implementation confirmed the practical viability of the models.

Conclusions:

  • The proposed fractional-order discrete memristor models exhibit unique hysteresis and memory characteristics.
  • Fractional-order discrete memristive systems demonstrate complex dynamics, controllable via memristor parameters.
  • FPGA implementation validates the potential of these discrete memristors for engineering applications.