Related papers: Optimal synchronization of directed complex networ…
We study optimal synchronization in networks of heterogeneous phase oscillators. Our main result is the derivation of a synchrony alignment function that encodes the interplay between network structure and oscillators' frequencies and can…
The multiplex network paradigm has been instrumental in revealing many unexpected phenomena and dynamical regimes in complex interacting systems. Nevertheless, most of the current research focuses on undirected multiplex structures, whereas…
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…
We study the synchronizability and the synchronization dynamics of networks of nonlinear oscillators. We investigate how the synchronization of the network is influenced by some of its topological features such as variations of the power…
In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are…
We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of…
By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree…
We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
We propose that negative degree correlation among nodes in a network of nonlinear oscillators, often detected in real world networks, is motivated by its positive effects on synchronizability. In so doing, we use a novel methodology to…
From the flashes of fireflies to Josephson junctions and power infrastructure, networks of coupled phase oscillators provide a powerful framework to describe synchronization phenomena in many natural and engineered systems. Most real-world…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
The extension of the master stability function (MSF) to analyze stability of generalized synchronization for coupled nearly identical oscillators is discussed. The nearly identical nature of the coupled oscillators comes from some parameter…
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 stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can…
Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in…
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…
Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far reaching applications in many domains,…
We consider two optimization problems on synchronization of oscillator networks: maximization of synchronizability and minimization of synchronization cost. We first develop an extension of the well-known master stability framework to the…
We provide a theoretical framework for quantifying the expected level of synchronization in a network of noisy oscillators. Through linearization around the synchronized state, we derive the following quantities as functions of the…