The dynamical response of a three-junction network II. Vortices

Mode-locking transitions and vortex flows in current-driven Josephson-junction arrays

“…In between these tongues, the behavior is quasiperiodic with two independent frequencies ͑QP 2 ), much as for an overdamped triangle driven by independent current sources. 18 This similarity of behavior is no coincidence. Indeed, with junctions 1-0 and 2-0 mode locked, the system behaves effectively like the overdamped triangle and the phase diagram of the former has embedded within it the entire phase diagram of the latter.…”

“…18 The i-⌬ phase diagram consists of a fixed-point steady-state regime, and an infinity of Arnold tongues which merge at the steady-state boundary. The behavior in the regions separating the tongues is quasiperiodic with two independent frequencies.…”

“…For mode locking ͓characterized by (w 12 ,w 23 ) ϭ(1, p 2 /q 2 )͔ in this region, the number of vortices injected by the drive through bond 2-3 in each repeating sequence of q 2 vortices is precisely q 2 Ϫp 2 . 18 Since there is no flow of vortices across bond 1-2, all the vortices, that leave the second plaquette through bond 2-0, have also to pass through bond 1-0. Hence, p 1 ϭq 1 ϭp 2 , as observed.…”

“…The motion of these systems is restricted to N tori and has been extensively studied. [18][19][20] As a result, the Nϭ2 case has come to be well understood ͑it gives rise to only two types of flows-periodic and quasiperiodic͒, and a number of facts have been discovered about the Nу3 case. 16,[21][22][23][24][25] In particular, it has been shown 23,24 that for a system with a three-frequency quasi-periodic ͑QP 3 ) attractor, there exist arbitrarily small C 2 perturbations, 26 which convert the attractor to one which is strange and structurally stable.…”

“…18 The underlying parameter space was mapped and each region interpreted in terms of vortices. This analysis was subsequently extended to an underdamped triangular network, 27 as well.…”