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  4. Chaotic dynamics of a new 7D memristor-based generator: computer modeling and circuit design

Chaotic dynamics of a new 7D memristor-based generator: computer modeling and circuit design

MMC.
2025;
Volume 12, Number 1
: pp. 116–131
https://doi.org/10.23939/mmc2025.01.116
Received: July 08, 2024
Accepted: September 26, 2024

Kopp M. I., Samuilik I.  Chaotic dynamics of a new 7D memristor-based generator: computer modeling and circuit design.  Mathematical Modeling and Computing. Vol. 12, No. 1, pp. 116–131 (2025)

Authors:
  1. M. I. Kopp
  2. I. Samuilik
1
Institute for Single Crystals, NAS Ukraine
2
Institute of Life Sciences and Technologies, Daugavpils University; Institute of Applied Mathematics, Riga Technical University

The paper introduces a new seven-dimensional (7D) chaotic system based on a memristor emulator created using a hyperbolic tangent function.  This system is derived from a six-dimensional (6D) dynamic system of equations that describes the process of magnetic field generation, serving as an alternative to the Rikitake dynamo, which explains the inversion of the magnetic field of the Earth and other celestial bodies.  The study analyzes the stability of equilibrium points in the new dynamical system.  The Lyapunov exponents spectrum and the Kaplan–Yorke dimension are calculated for fixed parameters of the 7D dynamical system.  The presence of a positive Lyapunov exponent demonstrates the chaotic behavior of the new 7D dynamic system, while the fractional Kaplan–Yorke dimension indicates the fractal structure of strange attractors.  Based on the results from Matlab–Simulink and LabVIEW models, a chaotic signal generator for the 7D chaotic memristive system is implemented in the Multisim environment.  The chaotic behavior simulation in the Multisim environment exhibits similar results to the simulations in the Matlab–Simulink and LabVIEW models.

memristor-based dynamic systems
chaotic behavior
computer simulation
circuit implementation
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