Related papers: Partial Synchronization and Partial Amplitude Deat…
We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic…
We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) random scale-free topology, (ii)…
A procedure is developed and tested to enforce synchronicity in a family of Stuart-Landau oscillators, coupled through a symmetric network. The proposed method exploits network plasticity, as an inherent non autonomous drive. More…
Amplitude death is a dynamical phenomenon in which a network of oscillators settles to a stable state as a result of coupling. Here, we study amplitude death in a generalized model of delay-coupled delay oscillators. We derive analytical…
We present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment-like external system. We develop a general stability analysis that is valid for any network…
The synchronous dynamics of an array of excitable oscillators, coupled via a generic graph, is studied. Non homogeneous perturbations can grow and destroy synchrony, via a self-consistent instability which is solely instigated by the…
We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in…
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…
Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
We study synchronization in delay-coupled oscillator networks, using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of super- or subcritical Hopf bifurcation) we derive analytical…
We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and…
Partially synchronized solitary states occur frequently when a synchronized system of networked oscillators is perturbed locally. Several asymptotic states of different frequencies can coexist at the same node. Here, we reveal the mechanism…
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
We investigate the synchronization features of a network of spiking neurons under a distance-dependent coupling following a power-law model. The interplay between topology and coupling strength leads to the existence of different…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous…
We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital…
Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons…