Related papers: Reliability of Coupled Oscillators II: Larger Netw…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
A networked oscillator based analysis is performed for periodic bluff body flows to examine and control the transfer of kinetic energy. Spatial modes extracted from the flow field with corresponding amplitudes form a set of oscillators…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the…
The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the…
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems.…
Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase…
The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows…
Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including…
Recent work in the area of interdependent networks has focused on interactions between two systems of the same type. However, an important and ubiquitous class of systems are those involving monitoring and control, an example of…
We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition, and…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
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…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
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…
The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…