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Research on fractional-order memory system signals based on Loop-By-Loop Progressive Iterative Method.

Li Xu1, Chuan Huang1, Guo Huang2

  • 1School of Electronic Information and Artificial Intelligence, Leshan Normal University, Leshan, China.

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|October 18, 2024
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Summary

A new Loop-By-Loop Progressive Iterative Method (LPIM) accurately analyzes fractional-order circuits. This novel approach was validated on fractance circuits and applied to Flux-Controlled Fractional-Order Memory Systems, revealing new insights into their behavior.

Keywords:
Flux-controlled fractional-order memory systemsFractanceFractional-order memory systems output signalsLoop-By-Loop Progressive Iterative Method

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Area of Science:

  • Electrical Engineering
  • Nonlinear Dynamics
  • Circuit Theory

Background:

  • Traditional methods for analyzing fractional-order circuits can be complex.
  • Fractional-order circuits exhibit unique behaviors not captured by integer-order models.
  • Novel analytical techniques are needed to fully understand these systems.

Purpose of the Study:

  • Introduce and validate the Loop-By-Loop Progressive Iterative Method (LPIM) for fractional-order circuit analysis.
  • Apply LPIM to a novel Flux-Controlled Fractional-Order Memory Systems (FFMS) model.
  • Predict common output characteristics of Fractional-Order Memory Systems (FMS).

Main Methods:

  • Developed the Loop-By-Loop Progressive Iterative Method (LPIM).
  • Applied LPIM and Laplace transform to analyze a fractance circuit.
  • Constructed a new Fractional-Order Memory Systems (FMS) model.
  • Simulated the FFMS using LPIM with a sinusoidal excitation signal.

Main Results:

  • LPIM results for fractance circuits were consistent with Laplace transform and existing theories.
  • The output signal of the FFMS exhibited two intersection points under sinusoidal excitation.
  • The FFMS output signal was modulated by the excitation signal's frequency.

Conclusions:

  • LPIM is a valid and effective method for analyzing fractional-order circuits.
  • The study provides the first simulation and analysis of FFMS output signals.
  • Predicted common output behaviors for FMS based on simulation results and theory.