Enhancement of network synchronizability via two oscillatory system

Abstract

Network's synchronization destabilizes at large coupling strength when its nodes exchange information by scalar coupling (few coordinates) instead of using vector coupling (all coordinates). This issue is commonly tackled by modifying the network topology like a ring network to Small World or Scale Free networks which increases the coupling cost and decreases the robustness. In the present work, we show that without any structural alteration even a large ring network in the nearest neighborhood configuration using only a single coordinate in the coupling, could be made synchronizable. The primary condition is that the node dynamics should be given by a pair of oscillators (say, two oscillatory system TOS) rather than by a conventional way of single oscillator (say, single oscillatory system). It has been found that TOS not only stabilizes the chaotic synchronization but also the hyperchaotic synchronization manifold (a major challenge in the field of secure communication wherein multi parameter BK method is needed). The frameworks of drive-response system and master stability function 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 (Rössler, 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 Rössler, intermediate for Chua and smaller for Lorenz. dsyn g ) limit the size of a synchronizable network, e.g. the synchronized state of a ring network having x 1 -coupled chaotic Rössler becomes unstable with the increase in N from 18 to 19 at dsyn g = 1.5. To tackle this issue of limited values of dsyn g , the network modification methods are generally used such as (1) adding the additional edges between the nodes deterministically (Pristine World) or/and stochastically (Small World) [5], (2) modifying the ring network topology to a synchronizable topology like a unidirectional tree network or a star network (a hub of Scale Free network) [6][7][8]. Practically these modifications could be considered as the distribution of overload among the nodes and theoretically these alterations imply the minimization of eigen-ratio (R) of the Laplacian/ coupling matrix (largest eigenvalue to the smallest nonzero eigenvalue). The concept of R minimization comes from the theory of master stability function (MSF) [9] which says that a complex network of size N is