Related papers: Ensemble order parameter equations in star network
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…
Can synchronization properties of a network of identical oscillators in the presence of noise be improved through appropriate rewiring of its connections? What are the optimal network architectures for a given total number of connections?…
Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal…
We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which *arbitrarily many* edge changes may occur in each round. Our algorithm significantly improves upon prior work in…
Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible…
We investigate the role of the spectral dimension $d_s$ in determining the universality of phase transitions on a complex network. Due to its structural heterogeneity, a complex network generally acts as a disordered system. Specifically,…
The synchronization of human networks is essential for our civilization, and understanding the motivations, behavior, and basic parameters that govern the dynamics of human networks is important in many aspects of our lives. Human ensembles…
Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto…
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…
The effect of phase-lag parameter in pairwise interactions has been a topic of great interest for long. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We…
We introduce a general scheme for constructing order parameters (OPs) by extracting generic patterns from the dominant Fock states of many-body ground states. While topological phases are traditionally characterized by non-local invariants,…
Numerical simulations of phase ordering under dissipative dynamics in a (2+1)-dimensional 3-vector model with O(3) symmetry are reported. The energy functional includes terms which stabilize the size of extended topological defects. They…
We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous…
Critical phenomena in complex networks, and the emergence of dynamical abrupt transitions in the macroscopic state of the system are currently a subject of the outmost interest. We report evidence of an explosive phase synchronization in…
We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…
A new network evolution model is introduced in this paper. The model is based on co-operations of $N$ units. The units are the nodes of the network and the co-operations are indicated by directed links. At each evolution step $N$ units…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
The aim of this paper is to derive macroscopic equations for processes on large co-evolving networks, examples being opinion polarization with the emergence of filter bubbles or other social processes such as norm development. This leads to…