Related papers: Interlayer antisynchronization in degree-biased du…
We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for…
In a recent study of chaos synchronization in symmetric complex networks [Pecora \textit{et al}., Nat. Commun. {\bf 5}, 4079 (2014)], it is found that stable synchronous clusters may coexist with many non-synchronous nodes in the…
We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability…
In this letter, we propose high order layered complex networks. The synchronization is discussed in detail. The relations of synchronization, individual coupling matrices and the intrinsic function of the uncoupled system are given. As…
The phenomenon of synchronization, where entities exhibit stable oscillations with aligned frequencies and phases, has been detected in diverse areas of natural science. It plays a crucial role in achieving frequency locking in multiple…
Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The method of averaging plays an important role in stability analysis, but the standard Lyapunov's second method is not applicable due to the lack of…
We study synchronization in scalar nonlinear systems connected over a linear network with stochastic uncertainty in their interactions. We provide a sufficient condition for the synchronization of such network systems expressed in terms of…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
By using the random interchanging algorithm, we investigate the relations between average distance, standard deviation of degree distribution and synchronizability of complex networks. We find that both increasing the average distance and…
Real world complex networks often exhibit multiplex structure, connecting entities from different aspects of physical systems such as social, transportation and biological networks. Little is known about general properties of such networks…
Previous research claimed or disclaimed the role of a small diameter in the synchronization of a network of coupled dynamical systems. We investigate this connection and show that it is two folds. We first construct two classes of networks,…
This paper investigates the stability and stabilization of diffusively coupled network dynamical systems. We leverage Lyapunov methods to analyze the role of coupling in stabilizing or destabilizing network systems. We derive critical…
The contradiction between the fact that many empirical networks possess power-law degree distribution and the finding that network of heterogeneous degree distribution is difficult to synchronize has been a paradox in the study of network…
Investigating relation between various structural patterns found in real-world networks and stability of underlying systems is crucial to understand importance and evolutionary origin of such patterns. We evolve multiplex networks,…
We study synchronization in delay-coupled oscillator networks, using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of super- or subcritical Hopf bifurcation) we derive analytical…
Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…
This Letter investigates the nature of synchronization in multilayered and multiplexed populations in which the interlayer interactions are randomly pinned. First, we show that a multilayer network constructed by setting up all-to-all…
Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these…
The coexistence of multiple types of interactions within social, technological and biological networks has moved the focus of the physics of complex systems towards a multiplex description of the interactions between their constituents.…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…