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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…
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…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of…
We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical…
We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
We present an equation-free computational approach to the study of the coarse-grained dynamics of {\it finite} assemblies of {\it non-identical} coupled oscillators at and near full synchronization. We use coarse-grained observables which…
We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh--Nagumo oscillators. For a large range of within- and between-network couplings, the…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
Modeling the behavior of coupled networks is challenging due to their intricate dynamics. For example in neuroscience, it is of critical importance to understand the relationship between the functional neural processes and anatomical…
Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ODEs with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlases they may be…
Complex networks often exhibit emergent behaviors, where simple dyadic interactions yield collective dynamics that cannot be explained by examining the system's units individually or in pairs. Understanding how redundant and synergistic…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…
Dynamical systems can be analyzed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within…
We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In…
Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…
Phase control of parametric modulation in coupled oscillator networks enables sculpting of dynamical states with desired spatiotemporal symmetries. Symmetry-aware Floquet analysis successfully predicts such states in linear systems, but…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…