Related papers: Laplacian Spectra as a Diagnostic Tool for Network…
We study the spectral zeta functions of the Laplacian on fractal sets which are locally self-similar fractafolds, in the sense of Strichartz. These functions are known to meromorphically extend to the entire complex plane, and the locations…
Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide…
We consider networks of coupled maps where the connections between units involve time delays. We show that, similar to the undelayed case, the synchronization of the network depends on the connection topology, characterized by the spectrum…
We study networks of noisy phase oscillators whose nodes are characterized by a random degree counting the number of its connections. Both these degrees and the natural frequencies of the oscillators are distributed according to a given…
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised…
We report the synchronization behavior in a one-dimensional chain of identical limit cycle oscillators coupled to a mass-spring load via a force relation. We consider the effect of periodic parametric modulation on the final synchronization…
The dynamical and structural aspects of cluster synchronization (CS) in complex systems have been intensively investigated in recent years. Here, we study CS of dynamical systems with intra and inter-cluster couplings. We propose new…
In this paper, we study the properties of two-dimensional lattices in the presence of non-Hermitian disorder. In the context of coupled mode theory, we consider random gain-loss distributions on every waveguide channel (on site disorder).…
In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…
While symmetry has been exploited to analyze synchronization patterns in complex networks, the identification of symmetries in large-size network remains as a challenge. We present in the present work a new method, namely the method of…
We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of…
The eigenvalues of the normalized Laplacian matrix of a network plays an important role in its structural and dynamical aspects associated with the network. In this paper, we study the spectra and their applications of normalized Laplacian…
Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a…
This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity)…
Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the…
This article proposes a first analysis of kernel spectral clustering methods in the regime where the dimension $p$ of the data vectors to be clustered and their number $n$ grow large at the same rate. We demonstrate, under a $k$-class…
The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic…
Pinning control of a complex network aims at forcing the states of all nodes to track an external signal by controlling a small number of nodes in the network. In this paper, an algebraic graph-theoretic condition is introduced to optimize…
We propose a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps. The magnetic Laplacian is a complex deformation of the well-known combinatorial…
In this paper, we investigate the factors that affect the synchronization of coupled oscillators on networks. By using the edge-intercrossing method, we keep the degree distribution unchanged to see other statistical properties' effects on…