Related papers: Link-disorder fluctuation effects on synchronizati…
Here we investigate the synchronization of networks of FitzHugh-Nagumo neurons coupled in scale-free, small-world and random topologies, in the presence of distributed time delays in the coupling of neurons. We explore how the…
In this research report, we examine the effects of small-world network organization on spike synchronization dynamics in networks of Izhikevich spiking units. We interpolate network organizations from regular ring lattices, through the…
We investigate the effect of preferentially connecting oscillators with similar frequency to each other in networks of coupled phase oscillators (i.e., frequency assortativity). Using the network Kuramoto model as an example, we find that…
Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…
It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [G\'omez-Garde\~nes \emph{et al.} Phys.Rev.Letts. 106, 128701 (2011)] and chaotic oscillators [Leyva \emph{et al.}…
In this study, we construct such systems with the Kuramoto model of globally coupled oscillators with time-delayed positive and negative couplings to explore the impact of coupling time delays in the collective frequency of synchronized…
This is the transcript of a talk given at the 1992 Complex Systems Summer School. The theory of large fluctuations of stochastically perturbed continuous-time dynamical systems is reviewed, and the large fluctuations of two stochastic…
This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
We introduce a system of pulse coupled oscillators that can change both their phases and frequencies; and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on…
In an all-to-all network of integrate-fire oscillators in which there is a disorder in the intrinsic firing rates of the neurons, we show that through spike timing-dependent plasticity the links which have the faster oscillators as…
We investigate the effect of quenched bond-disorder on the anisotropic spin-1/2 (XXZ) chain as a model for disorder induced quantum phase transitions. We find non-universal behavior of the average correlation functions for weak disorder,…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…
We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed…
Spontaneous time-reversal symmetry breaking in superconductors with competing non-degenerate pairing channels is an exotic quantum phase transition that could give rise to robust topological superconductivity and unusual magnetism. It is…
Heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators. Scale-free networks display a great deal of heterogeneity, containing a few nodes, termed hubs,…
We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal…
The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the…
Density-wave instabilities have been observed and studied in a multitude of materials. Most recently, in the context of unconventional superconductors like the iron-based superconductors, they have excited considerable interest. We analyze…
80% of all Renewable Energy Power in Germany is installed in tree-like distribution grids. Intermittent power fluctuations from such sources introduce new dynamics into the lower grid layers. At the same time, distributed resources will…