Stefano Boccaletti

Synchronization in complex networks with age ordering

The propensity for synchronization is studied in a complex network of asymmetrically coupled units, where the asymmetry in a given link is determined by the relative age of the involved nodes. In growing scale-free networks synchronization is enhanced when couplings from older to younger nodes are dominant. We describe the requirements for such an effect in a more general context and compare with the situations in non growing random networks with and without a degree ordering.

Explosive Synchronization in Adaptive and Multilayer Networks

At this time, explosive synchronization (ES) of networked oscillators is thought of as being rooted in the setting of specific microscopic correlation features between the natural frequencies of the oscillators and their effective coupling strengths. We show that ES is, in fact, far more general and can occur in adaptive and multilayer networks in the absence of such correlation properties. We first report evidence of ES for single-layer networks where a fraction f of the nodes have links adaptively controlled by a local order parameter, and we then extend the study to a variety of two-layer networks with a fraction f of their nodes coupled with each other by means of dependency links. In the latter case, we give evidence of ES regardless of the differences in the frequency distribution, in the topology of connections between the layers, or both. Finally, we provide a rigorous, analytical treatment to properly ground all of the observed scenarios and to advance the understanding of the actual mechanisms at the basis of ES in real-world systems.

SYNCHRONIZATION IN NETWORKS OF SLIGHTLY NONIDENTICAL ELEMENTS

We study synchronization processes in networks of slightly nonidentical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in parameters can be properly modeled by a noise term affecting the stability of the synchronous invariant solution emerging for identical systems when the parameter is set at the mean value of the original distribution.

Experimental observations of synchronization interfaces in networks of oscillators

In complex networks, beyond the appearance of a global synchronized state, cases in which clusters of synchronized nodes form can also be observed. In such cases, a specific dynamical behavior in the nodes constituting the interface between clusters of synchronized units is obtained. In this paper, a network of nonlinear circuits is investigated with the aim of giving experimental evidences of the behavior of interface nodes oscillating with an instantaneous frequency varying in time between those of the network communities.

Pattern competition in a high-power CO2 laser due to optogalvanic modulation of the pump profile

Experimental evidence of periodic alternation of different transverse modes in a high-power CO 2 laser is interpreted in terms of local cooling of the discharge column, which corresponds to the maximum emitted intensity. Optogalvanic coupling between emitted intensity and local discharge impedance values yields a transverse redistribution of discharge current and, hence, of laser gain. Thus, besides the fast feedback provided by the cavity, with high-power lasers one must account also for a slow global feedback because of the optogalvanic effects.

Topological stability criteria for networking dynamical systems with Hermitian Jacobian

The central theme of complex systems research is to understand the emergent macroscopic properties of a system from the interplay of its microscopic constituents. The emergence of macroscopic properties is often intimately related to the structure of the microscopic interactions. Here, we present an analytical approach for deriving necessary conditions that an interaction network has to obey in order to support a given type of macroscopic behaviour. The approach is based on a graphical notation, which allows rewriting Jacobis signature criterion in an interpretable form and which can be applied to many systems of symmetrically coupled units. The derived conditions pertain to structures on all scales, ranging from individual nodes to the interaction network as a whole. For the purpose of illustration, we consider the example of synchronization, specifically the (heterogeneous) Kuramoto model and an adaptive variant. The results complete and extend the previous analysis of Do et al. ( 2012 Phys. Rev. Lett. 108 , 194102).