Nonlinear dynamics of a Josephson oscillator with acosφterm driven by dc- and ac-current sources

The bifurcations and transitions to chaos in the dc- and ac-current biased Josephson junction are investigated by numerically integrating the Stewart-McCumber model with an interference "$\epsilon cos\phi$" term. The initial transient method is proposed and successfully applied to construct the model one-dimensional (1D) maps which can reproduce the essential characteristics of the results of numerical solutions. It is shown that the effects of the "$\epsilon cos\phi$" term are crucial to the bifurcation mechanism and chaotic responses of nonlinear dynamics, i.e., successive direct and reverse $2^n$ bifurcations (period-doubling and -halving bifurcations), breakdown of the negative Schwarzian condition, and tangent bifurcations. Then the value of $\epsilon$ can be estimated by bifurcation diagrams, e.g., to be -0.95mp 0.01 for the Cirillo-Pedersen experiment. The abnormal situation occurs at $\epsilon =-0.977\mathrm{}65$ where Feigenbaum's universal constant $\delta$ is replaced by $\sqrt{\delta }$. The transfer crises previously found in the 1D map by the present authors are first observed in the realistic system, and the discontinuous change of power spectrum associated with the interior crisis is also shown.