Related papers: Correspondence between phase oscillator network an…
We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.
Demographic oscillators are individual-based systems exhibiting temporal cycles sustained by the stochastic dynamics of the microscopic interacting particles. We here use the example of coupled predator-prey oscillators to show that…
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin…
We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors,…
We investigate coherent oscillations in large scale transmission power grids, where large groups of generators respond in unison to a distant disturbance. Such long wavelength coherent phenomena are known as inter-area oscillations. Their…
We have investigated the role that different connectivity regimes play on the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random connectivity…
In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling…
Inspired by Axelrod's model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The…
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial…
Oscillatory media can exhibit the coexistence of synchronized and desynchronized regions, so-called chimera states, for uniform parameters and symmetrical coupling. In a phase-balanced chimera state, where the totals of synchronized and…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
This thesis focuses on the XY model, the simplest vector spin model, used for describing numerous physical systems. It is studied for different sources of quenched disorder: random couplings, random fields, or both them. The belief…
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 explosive synchronization, a phenomenon characterized by first-order phase transitions between incoherent and synchronized states in networks of coupled oscillators. While explosive synchronization has been the subject of many…
Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…
We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We…
We study the asymptotic emergent dynamics of two models that can be thought of as extensions of the well known Schr\"odinger-Lohe model for quantum synchronization. More precisely, the interaction strength between different oscillators is…
The damped driven nonlinear Schr\"odinger equation (NLSE) has been used to understand a range of physical phenomena in diverse systems. Studying this equation in the context of optical hyper-parametric oscillators in anomalous-dispersion…
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…
We study the phase diagram of the standard pair approximation equations for two different models in population dynamics, the susceptible-infective-recovered-susceptible model of infection spread and a predator-prey interaction model, on a…