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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.
Entropy (Basel, Switzerland)
|June 24, 2022
Summary
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.
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.
Keywords:
digital circuitsdiscrete modeling of memristorfractional-order differencememristive systemmemristorMore Related Videos
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