On-off intermittency from a ring of four-coupled PLLs

Abstract

In this paper, on–off intermittency observed in a ring of four-coupled PLLs is studied theoretically and experimentally. There exists a semistable invariant manifold in the phase space of this system. The orbit is irregularly transitioning between the laminar state constraint to the invariant manifold and the burst state jumping outward. In this research, the transversal Lyapunov exponent is first computed. It is then pointed out that on–off intermittency can appear with many parameter values. As an example, it is made clear from the calculations of several statistical characteristic quantities such as the local transversal expansion rate and laminar phase distribution that the intermittency generated with one of these parameters is an on–off intermittency. Further, by studying the bifurcation of the periodic solution on an invariant manifold, the generating mechanism of this on–off intermittency is made clear geometrically. © 2000 Scripta Technica, Electron Comm Jpn Pt 2, 83(2): 26–34, 2000