Related papers: Synchronization is optimal in non-diagonalizable n…
In this paper we use the master stability function (MSF) for nearly identical dynamical systems obtained in the previous paper to construct optimized networks (ONs) which show better synchronizability. Nearly identical nature is the result…
By a model of coupled phase oscillators, we show analytically how synchronization in {\em non-identical} complex networks can be enhanced by introducing a proper gradient into the couplings. It is found that, by pointing the gradient from…
We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…
We investigate the existence of an optimal interplay between the natural frequencies of a group chaotic oscillators and the topological properties of the network they are embedded in. We identify the conditions for achieving phase…
A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical…
In networks of identical linear oscillators (e.g. pendulums undergoing small vibrations) coupled through both dissipative connectors (e.g. dampers) and restorative connectors (e.g. springs) the relation between asymptotic synchronization…
We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
In these notes we study synchronizability of dynamical processes defined on complex networks as well as its interplay with network topology. Building from a recent work by Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)], we use a…
Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted…
We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
In the study of network synchronization, an outstanding question of both theoretical and practical significance is how to allocate a given set of heterogenous oscillators on a complex network in order for improving the synchronization…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
We present the $\delta$-Synchronizer, which works in non-synchronous dynamic networks under minimal assumptions. Our model allows for arbitrary topological changes without any guarantee of eventual global or partial stabilization and…
Synchronization is essential for the operation of AC power systems: All generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of…
Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions have the power-law form. In this paper, we investigate the synchronization phenomena in a scale-free…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…
The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…