Related papers: Critical parameters of the synchronisation's stabi…
We study spatially periodic orbits for a coupled map lattice of sine circle maps with nearest neighbour coupling and periodic boundary conditions. The stability analysis for an arbitrary spatial period k is carried out in terms of the…
There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…
Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with $m$-separation provide classes of symmetric graphical independence models that are closed under…
A metrized graph is a compact singular 1-manifold endowed with a metric. A given metrized graph can be modelled by a family of weighted combinatorial graphs. If one chooses a sequence of models from this family such that the vertices become…
This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…
We introduce merge-width, a family of graph parameters that unifies several structural graph measures, including treewidth, degeneracy, twin-width, clique-width, and generalized coloring numbers. Our parameters are based on new…
We study bifurcations of the completely synchronized state in a continuum limit (CL) for the Kuramoto model (KM) of identical oscillators with two-mode interaction depending on two graphs. Here one of the graphs is uniform but may be…
We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of…
Let $\Gamma$ be a locally finite graph, $L$ the normalized Laplacian of $\Gamma$. If $\Gamma$ is uniformy locally finite, i.e. if each vertex has no more than $d$ adjacent vertices, then the matrix of $L$ (with respect to the standard…
Coordination sequences of periodic and quasiperiodic graphs are analysed. These count the number of points that can be reached from a given point of the graph by a number of steps along its bonds, thus generalising the familiar coordination…
In our previous work [Chiba, Medvedev, arXiv:1612.06493], we initiated a mathematical investigation of the onset of synchronization in the Kuramoto model (KM) of coupled phase oscillators on convergent graph sequences. There, we derived and…
This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state…
Three major properties of the chaotic dynamics of the standard map, namely, the measure \mu of the main connected chaotic domain, the maximum Lyapunov exponent L of the motion in this domain, and the dynamical entropy h = \mu L are studied…
The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning…
We study the critical features of coupling parameter in the synchronization of neural networks with diluted synapses. Based on simulations, the exponential decay form is observed in the extreme case of global coupling among subsystems and…
The transition to global synchronization in coupled dynamical systems is governed by the interplay between coupling strength and structural topology. Although abrupt, first-order-like synchronization transitions have been extensively…
The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to…
We present hierarchy of one and many-parameter families of elliptic chaotic maps of cn and sn types at the interval [0,1]. It is proved that for small values of k the parameter of the elliptic function, these maps are topologically…
In this paper, we consider the approximate weighted graph matching problem and introduce stable and informative first and second order compatibility terms suitable for inclusion into the popular integer quadratic program formulation. Our…
We study harmonic mappings from a Riemannian manifold $N$ into a principal $G$-bundle $P$ endowed with a $G$-invariant Riemannian metric (i.e. a Kaluza-Klein metric). These morphisms are called Kaluza-Klein harmonic maps and naturally lead…