Effect of a periodic perturbation on radio frequency model of Josephson junction

By using the analytical method of Mel'nikov the qualitative behavior of the single differential equation
\ddot{x}+\delta \dot{x}- \alpha \sin x = f_{0} + f_{1} \sin(\omega t), \dot{x}\stackrel{\Delta}{=} \frac{dx}{dt}
where
\delta > 0, \alpha > 0, f_{0} \geq 0, f_{1} > 0, \omega > 0
is studied. The parameter space
(\delta, \alpha, f_{0}, f_{1}, \omega )
of the nonlinear oscillator (A) is decomposed by the threshold curve into two regions, where significantly different behavior of oscillations occurs. In the first part of the parameter space the existence of chaotic solutions of (A) is possible, whereas in the second part of the parameter space only regular oscillations are expected. A radio frequency network modeling the very high-frequency (VHF) phenomena in current driven Josephson junction with capacitance but without dc bias current is described. The results of the measurements of the frequency spectrum of voltage oscillations are presented. The theoretical predictions and experimental data are not in disagreement. In order to pinpoint exactly the parameter subspace of the nonlinear oscillator (A) with chaos, a more general and detailed analytical criterium than Mel'nikov method is needed.