Enhancement of Network Synchronizability via Two Oscillatory System

Abstract

The loss of synchronizability at large coupling strength is of major concern especially in the fields of secure communication and complex systems. Because theoretically, the coupling mode that can surely stabilize the chaotic/hyperchaotic synchronized state is vector coupling (using all the coordinates) which is in contrast to the practical demand of information exchange using lesser number of coordinates (commonly via a single coordinate). In the present work, we propose that if the node dynamics are given by a pair of oscillators (say, {\it two oscillatory system} TOS) rather than by a conventional way of single oscillator (say, {\it single oscillatory system} SOS), then the information exchange via a single coordinate could be sufficient to stabilize the chaotic/hyperchaotic synchronization manifold at large coupling strength. The frameworks of drive-response system and Master Stability Function (MSF) have been used to study the TOS effect by varying TOS parameters with and without feedback (feedback means quorum sensing conditions). The TOS effect has been found numerically both in the chaotic (R{ö}ssler, Chua and Lorenz) and hyperchaotic (electrical circuit) systems. However, since threshold also increases as a side effect of TOS, the extent of $β$ enhancement depends on the choice of oscillator model like larger for R{ö}ssler, intermediate for Chua and smaller for Lorenz.