Comparison of Bifurcation Diagrams for Numerical and Analog Chaotic Systems

Researchers studying chaos theory often implement electrical circuits as analog solvers of chaotic equations. Analog circuits allow obtaining chaotic waveforms unaffected by any numerical method and may have practical applications. However, in almost all studies, the bifurcation diagrams are plotted using a computer simulation rather than using measurements in analog circuits. This paper proposes an approach for bifurcation analysis of circuits using the NI ELVIS controller and LabVIEW software. Plotting circuit bifurcation diagrams, we found that it is difficult to establish a good correspondence between the circuit and the numerical model dynamics, even with careful component selection and utilizing precision op-amps. This result indicates a need of validating developed chaotic circuits in hardware.