Chaotic Synchronization in a Five-Star-Coupled Phase-Locked Loop System

Abstract

This paper describes a chaotic synchronization phenomenon observed experimentally in a five-star-coupled phase-locked loop (PLL) oscillator system. This system consists of five PLLs connected in the shape of a star. The state in this system itinerates between the completely synchronized state, in which all PLL oscillators synchronize, and the disordered state, in which all PLLs oscillate individually, via the partially synchronized state. The time-series of the voltage difference between arbitrary two PLL oscillators shows the on-off intermittency. When such a chaotic itinerancy occurs, the distribution function of the duration time of the completely synchronized state is expressed as a −\\frac32 power law which is quite similar to the distribution function of the laminar duration time in the on-off intermittency.