Chaos along the rc-branch of RLC-shunted intrinsic Josephson junctions

The appearance of chaos along the “charged” resonance circuit branch of the current-voltage characteristics is examined in a model of intrinsic Josephson junctions shunted by resistive, inductive and capacitive circuit elements. Detailed numerical simulations of the electric charge density, current-voltage characteristics and various chaos indicators, such as Lyapunov exponents and Poincaré sections are performed over a wide range of relevant system parameters. In mapping the parameter space, several distinctly different regions are found: some completely regular, while others are dominated by chaos, where the rc-frequency determines the appearance and properties of those regions. At higher values of the rc-frequency chaos appears at first over relatively narrow regions at the lower-current end of the rc-branch. As the rc-frequency is lowered, the chaotic region at the lowered-current end of the rc-branch may becomes wider, depending sensitively on the combination of system parameters. Examination of the metric entropy and maximal Kaplan–Yorke dimension shows that the dimensions of the chaotic attractors associated with the chaos do not plateau, as in the overdamped case, but surprisingly increase indefinitely with the number of junctions, indicating that the system is capable of truly high-dimensional chaos. The onset of the chaos along the rc-branch is found to occur via a two-frequency quasi-periodic route. Our results provided a guide for specific parameter combinations that could minimize the chaos, thereby making certain applications potentially more viable