Electronic simulation and microcontroller real implementation of an autonomous chaotic and hyperchaotic system made of a Colpitts-Josephson junction like circuit

Most of the simple Josephson junction (JJ) based circuits with chaotic behavior found in the literature are nonautonomous. Hyperchaotic JJ-based circuits are often either driven by an external force or result from coupling chaotic circuits. An autonomous simple circuit based on Josephson junction active element (JJ), with exactly three physical energy storage tanks, is proposed and analyzed in this paper. This Colpitts-like CLC circuit, though operating at low frequencies, can generate hyperchaotic signals when its nonlinear element is a resistive–capacitive–inductance shunted junction (LRCLSJ) model. Two equilibrium points are found, and their stability analysis is investigated. The proposed circuit displays Hopf bifurcation, periodic oscillations, chaotic and hyperchaotic attractors. The electronic implementation of the proposed circuit using OrCAD-PSpice software is presented to confront the numerical simulations results. A good qualitative agreement is revealed by comparing the analog and numerical simulations results. At last, the microcontroller real implementation is presented using Arduino UNO board. The results obtained are in good agreement with the numerical simulation results.