Abstract <p>The phase dynamics of two Josephson junctions connected in series and subjected to a time-varying magnetic field is explored. It is shown that periodical modulation of the magnetic flux, which determines the effective energy of an united Josephson junction, can lead to parametric instability and chaotic phase dynamics. Using computer simulations, it is demonstrated that in the chaotic regime, the phase of a dissipation-free superconducting device exhibits some novel phenomena. These include capture into resonance and “coverage” of the separatrix by a stochastic layer. We briefly discuss the possible application of the findings.</p>