Chaotic synchronisation in a four-coupled phase-locked loop system

The paper describes chaotic synchronisation, observed both experimentally and numerically, in a four-coupled phase-locked loop (PLL) system. The system consists of four PLLs and four couplers, constructed with four operational amplifiers. Each subsystem shows chaos and is described by a set of differential equations with seven degrees of freedom. When the synchronisation behaviour among these subsystems is observed, it is found that a subsystem easily synchronises with a subsystem positioned diagonally opposite, but hardly does so with adjacent subsystems. The on-off intermittency is observed for the difference between a couple of diagonally positioned subsystems. The chaotic transition of synchronised states in two diagonal pairs is investigated. From calculation of the local transverse Lyapunov exponent, it is considered that two hyperplanes exist in the phase space, and the phase point itinerates via the two planes