article · Journal of Electrical Systems and Information Technology
Nonlinear resistor-capacitor-inductor Josephson junction systems with hysteretic iron cores display intricate dynamical properties. By modelling the nonlinear inductor through a tangent interference term, the system reveals a rich set of complex physical behaviours. Numerical simulations using standard bifurcation diagrams, Fast Fourier Transform spectrums, and phase portraits confirm the presence of excitable modes, regular spiking, periodic bursting, and both chaotic and periodic attractors. To bridge theoretical modelling and practical experimentation, a digital microcontroller implementation of the piecewise resistor-capacitor-inductor-shunted circuit was developed. The physical microcontroller output closely reproduces the behaviours observed in software simulations, proving that accessible digital hardware can accurately emulate complex superconducting electronic phenomena for educational demonstrations and technical study.
Josephson junctions are fundamental components in superconducting electronics, yet studying their physical hardware requires specialised, costly laboratory conditions. Demonstrating that standard microcontrollers can accurately emulate their nonlinear, chaotic, and spiking dynamics offers a low-cost, accessible method for researchers, educators, and students to analyse complex circuit behaviours without needing specialised cryogenic experimental apparatus.
The microcontroller implementation is targeted at educational environments and engineering applications, offering engineers and technical trainees an accessible tool to emulate complex nonlinear dynamics. Because the work focuses on verifying digital hardware emulation against numerical models, it represents an early-stage development rather than a commercial product ready for market deployment.
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Abstract In this work, the modelling and microcontroller implementation of Nonlinear Resistor-Capacitor-Inductor Josephson Junction (RCLSJJ) with Hysteretic Iron-Core is investigated. The nonlinear inductor is modeled using a tangent interference term. In the first part of this study, we analyze the Josephson junction model with a nonlinear inductor. The dynamical behaviors of the system are investigated using classical tools such as one-parameter bifurcation diagrams, Fast Fourier Transform (FFT) spectrums, and phase portraits. Numerical simulations performed in MATLAB reveal that the JJ-based nonlinear inductor exhibits a variety of behaviors, including excitable modes, regular spiking, periodic bursting, chaotic attractors, and periodic attractors. To support both engineering applications and educational purposes, a microcontroller-based implementation of the Piecewise Resistor-Capacitor-Inductor-Shunted Josephson Junction (PRCL-SJJ) circuit is developed. The results from the digital implementation closely match those obtained from numerical simulations.
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DOI: 10.1186/s43067-026-00392-4
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