MULTIPLE ATTRACTORS AND PERIODIC TRANSIENTS IN SYNCHRONIZED NONLINEARCIRCUITS

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.