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Updated: Jun 12, 2025

Assembly and Characterization of Biomolecular Memristors Consisting of Ion Channel-doped Lipid Membranes
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Dynamic Effects Analysis in Fractional Memristor-Based Rulkov Neuron Model.

Mahdieh Ghasemi1, Zeinab Malek Raeissi1, Ali Foroutannia2

  • 1Neural Engineering Laboratory, Department of Biomedical Engineering, University of Neyshabur, Neyshabur 9319774446, Iran.

Biomimetics (Basel, Switzerland)
|September 27, 2024
PubMed
Summary

Researchers developed a fractional memristor Rulkov neuron model, enhancing neural function analysis. This new model improves heritable properties, multi-time scale activity, and firing frequency responses, offering better synchronization in neural networks.

Keywords:
Rulkov mapchaotic systemsdiscrete fractional orderdiscrete memristorsynchronization of two coupled neurons

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Area of Science:

  • Computational Neuroscience
  • Nonlinear Dynamics
  • Fractional Calculus

Background:

  • Complex nervous system modeling relies on mathematical neuron models like Fitzhugh-Nagumo and Hodgkin-Huxley.
  • These models' complexity hinders detailed neural function analysis.
  • The discrete Rulkov model offers a simpler approach to studying neuronal dynamics.

Purpose of the Study:

  • Introduce a novel fractional memristor Rulkov neuron model.
  • Investigate dynamic effects and improvements by combining memristors and fractional derivatives.
  • Enhance neuron modeling for more accurate biophysical effect estimation.

Main Methods:

  • Combined a Rulkov neuron model with a memristor.
  • Evaluated system parameters using bifurcation diagrams and the 0-1 chaos test.
  • Applied a discrete fractional-order approach to the Rulkov memristor map and analyzed coupled systems.

Main Results:

  • The fractional memristor Rulkov model exhibits tonic, periodic, and chaotic firing behaviors.
  • Fractional order significantly impacts system dynamics and enhances synchronization.
  • Improved generation of heritable properties and multi-time scale activity compared to full-order models.

Conclusions:

  • The fractional memristor Rulkov neuron model offers enhanced accuracy and performance.
  • Fractional calculus and memristors effectively improve discrete neuron models.
  • This combined approach is valuable for modeling biophysical effects in neural networks.