In this paper, on-off intermittency observed in a ring of four-coupled PLLs
is studied theoretically and experimentally. There exists a semistable inv
ariant manifold in the phase space of this system. The orbit is irregularly
transitioning between the laminar state constrains to the invariant manifo
ld and the burst state jumping outward. In this research, the transversal L
yapunov exponent is first computed. It is then pointed out that on-off inte
rmittency can appear with many parameter values. As an example, it is made
clear from the calculations of several statistical characteristic quantitie
s such as the local transversal expansion rate and laminar phase distributi
on that the intermittency generated with one of these parameters is an on-o
ff intermittency. Further, by studying the bifurcation of the periodic solu
tion on an invariant manifold, the generating mechanism of this on-off inte
rmittency is made clear geometrically. (C) 2000 Scripts Technica.