Related papers: Comment on "Synchronization dynamics in non-normal…
This chapter presents a view of a non-autonomous oscillator as a mapping from input functions of time to a circle of possible solutions (state functions of time). It indicates how this view encompasses chronotaxic systems and enables one,…
Networks of coupled nonlinear oscillators have been used to model circadian rhythms, flashing fireflies, Josephson junction arrays, high-voltage electric grids, and many other kinds of self-organizing systems. Recently, several authors have…
We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
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…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
In this paper, we study the problem of synchronization with stochastic interaction among network components. The network components dynamics is nonlinear and modeled in Lure form with linear stochastic interaction among network components.…
This paper gives sufficient conditions for having complete synchronization of oscillators in connected undirected networks. The considered oscillators are not necessarily identical and the synchronization terms can be nonlinear. An…
In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…
In this article I investigate the novel synchronization behaviors of evolving pulse-coupled oscillator networks. Unlike previous models, the time-varying mechanism is inspired by neural network development, where seldom used links die out…
A small-world network (SW) of similar phase oscillators, interacting according to the Kuramoto model is studied numerically. It is shown that deterministic Kuramoto dynamics on the SW networks has various stable stationary states. This 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…
In this paper, the relationship between the network synchronizability and the edge distribution of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network sychronizability.…
The most profound effect of disorder on the elastic response of solids is the nonaffinity of local displacements whereby the atoms (particles, network junctions) do not simply follow the macroscopic strain, as they do in perfect crystals,…
We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10-200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level…