Bifurcations and Hyperchaos from a DC Driven nonidentical Josephson Junction System

The dynamics of a resistively coupled system of nonidentical Josephson junctions (JJ) with dc feedings is explored theoretically. The effects of system parameters on the dynamic features are defined and equilibrium features of the system of equations are explored in such a nonidentical JJ system for the first time. By using center manifold reduction, the inverse of coupling resistance Rcp is considered as the main bifurcation parameter. The bifurcation at the vicinity of the equilibrium point is found to be transcritical, stable and unstable regimes are also indicated analytically. It is observed that the amplitudes of the output voltages on the coupling resistance Rcp are changeable and mostly uncorrelated for two parts of superconducting junction system. Such a system exhibits very rich dynamics from periodic to chaotic behavior for certain parameter sets. While the regular characteristics are observed for moderate and lower feeding currents, chaotic and highly-complex patterns are obtained for relatively higher values of them. Besides, a wider hyperchaotic region is found for wide ranges of parameters after the determination of phase diagrams compared to the earlier studies. The nonidentical nature of JJs governs the complicated dynamics on the phase space. The present circuitry can be utilized for various purposes such as stable, chaotic or hyperchaotic behavior depending on the parameters Ii and Rcp.