Numerical Simulation of RCSJ Model for Josephson Junction: AC/DC I-V Characteristics and Nonlinear Chaotic Phenomena

This study presents a detailed numerical simulation investigation using MATLAB to analyze the AC/DC current-voltage characteristics and nonlinear chaotic phenomena in the RCSJ model of Josephson Junctions. The implementation utilizes numerical integration techniques through MATLAB's ode solvers to obtain solutions for the nonlinear differential equations governing the system. We systematically examined how various parameters in the RCSJ model influence Josephson junction behavior, employing parameter sweeps and stability analysis algorithms. The research includes comprehensive analysis of I-V characteristic generation mechanisms and chaos formation processes, with MATLAB scripts generating AC/DC I-V characteristic curves, phase portraits of the nonlinear differential equations, and bifurcation diagrams illustrating the transition to chaos via period-doubling bifurcations and intermittency principles. Additional computational outputs include Poincaré sections for state space analysis and power spectra obtained through Fast Fourier Transform (FFT) implementations, providing complete characterization of the nonlinear dynamics.