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We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched random frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically…
Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a…
This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
Models of coupled oscillators are useful in describing a wide variety of phenomena in physics, biology and economics. These models typically rest on the premise that the oscillators are weakly coupled, meaning that amplitudes can be assumed…
The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…
The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force $f$ and its frequency $\Omega$. We first examine the stability of the steady state…
We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
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,…
The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the…
The collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied when the natural frequency distribution does not possess an even symmetry with respect to the average natural frequency…
We introduce a model to study the effect of degree-frequency correlations on synchronization in networks of coupled oscillators. Analyzing this model, we find several remarkable characteristics. We find a stationary synchronized state that…
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two…
We study the phase synchronization between collective rhythms of fully locked oscillator groups. For weakly interacting groups of two oscillators with global sinusoidal coupling, we analytically derive the collective phase coupling…
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 the emergence of phase-locking for Winfree oscillators under the effect of inertia. It is known that in a large coupling regime, oscillators governed by the deterministic second-order Winfree model with inertia converge to a unique…
We investigate coupled identical phase oscillators with scale-free distribution of coupling strength. It is shown that partially locked states can occur due to the inhomogeneity in coupling and some properties of the coupling function.…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…