I study a pair of synchronized nonlinear circuits which may be periodi
c or chaotic. The circuits are synchronized by a one-way driving signa
l from the drive circuit to the response circuit. Because the nonlinea
rities are symmetric about zero, the drive circuit has two periodic at
tractors. When the value of a bifurcation parameter is above a certain
threshold, the response circuit also has two periodic attractors, one
in-sync with the drive and one out-of-sync. Below the threshold, the
drive circuit still has two attractors but the response circuit has on
ly one attractor, the in-sync attractor. If the response circuit is st
arted in the basin of attraction of the former out-of-sync attractor,
a long periodic transient (many cycles long) is seen. (C) 1998 Publish
ed by Elsevier Science B.V.