Opposed (hammerhead) bifurcations in the resonant lineshape of a strongly driven SQUID ring-tank circuit system

In this paper we describe very unusual paired bifurcations which can appear in the resonance curve of a coupled SQUID ring-radio frequency (rf) tank circuit system when the rf flux at the ring is comparable to Phi(0) (= h/2e). We demonstrate that the position of these bistabilities is controlled by the static magnetic flux Phi(xstat) applied to the ring, with simple bistable regions being observed on the lower or upper side of the resonance when (for n integer) Phi(xstat), is close to n Phi(0) or (n + 1/2) Phi(0), respectively. More interestingly, we show that for values of Phi(x) close to (n +/- 1/4) Phi(0) this resonance exhibits bistability on both its lower and upper sides. We discuss this very unusual phenomenon in terms of the non-linear equation of motion for the coupled system. (C) 1997 Elsevier Science B.V.