Related papers: Comment on "Synchronization dynamics in non-normal…
Interactions among units in complex systems occur in a specific sequential order thus affecting the flow of information, the propagation of diseases, and general dynamical processes. We investigate the Laplacian spectrum of temporal…
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize…
In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling…
In many real-world systems, partial synchronization is the dominant dynamical regime and, in systems such as the brain, is often accompanied by collective oscillations in which multiple overlapping modes interact to produce complex rhythmic…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
We note that building a magnetic Laplacian from the Markov transition matrix, rather than the graph adjacency matrix, yields several benefits for the magnetic eigenmaps algorithm. The two largest benefits are that the embedding becomes more…
Many oscillator networks are multistable, meaning that different synchronization states are realized depending on the initial conditions. In this paper, we numerically analyze a ring network of phase oscillators, in which synchronous states…
We investigate the equilibria of a random model network exhibiting extensive chaos. In this regime, a large number of equilibria is present. They are all saddles with low-dimensional unstable manifolds. Surprisingly, despite network's…
This work focuses on exploring the potential benefits of introducing a nonlinear Laplacian in Sheaf Neural Networks for graph-related tasks. The primary aim is to understand the impact of such nonlinearity on diffusion dynamics, signal…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
Neural circuits exhibit structured connectivity, including an overrepresentation of reciprocal connections between neuron pairs. Despite important advances, a full understanding of how such partial symmetry in connectivity shapes neural…
Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization…
We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance in power-grids where energy is either…
The dynamics of networks of neuronal cultures has been recently shown to be strongly dependent on the network geometry and in particular on their dimensionality. However, this phenomenon has been so far mostly unexplored from the…
To describe the flow of a miscible quantity on a network, we introduce the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. This is a natural description of an array of inductances and…
We consider bosonic quantum complex networks as structured finite environments for a quantum harmonic oscillator and investigate the interplay between the network structure and its spectral density, excitation transport properties and…
Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling.…
Most real-world networks display not only a heterogeneous distribution of degrees, but also a heterogeneous distribution of weights in the strengths of the connections. Each of these heterogeneities alone has been shown to suppress…
This work introduces the concept of tangent space regularization for neural-network models of dynamical systems. The tangent space to the dynamics function of many physical systems of interest in control applications exhibits useful…