Related papers: Recent Advances in Coupled Oscillator Theory
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,…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
For asymptotically periodic systems, a powerful (phase) reduction of the dynamics is obtained by computing the so-called isochrons, i.e. the sets of points that converge toward the same trajectory on the limit cycle. Motivated by the…
We present a direct comparison studying equilibration through kinetic theory at weak coupling and through holography at strong coupling in the same set-up. The set-up starts with a homogeneous thermal state, which then smoothly transitions…
We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
A long-standing expectation is that two repulsively coupled oscillators tend to oscillate in opposite directions. It has been difficult to achieve complete synchrony in coupled identical oscillators with purely repulsive coupling. Here, we…
Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now…
Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's…
The dynamical properties of a diluted fully-inhibitory network of pulse-coupled neurons are investigated. Depending on the coupling strength, two different phases can be observed. At low coupling the evolution rapidly converges towards…
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
Collocated adaptive control of underactuated systems is still a main concern for the control community, all the more so because the collocated dynamics is no longer linear with respect to the constant base parameters. This work extends and…
Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for…
The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing,…
We present a general approach to the study of synchrony in networks of weakly nonlinear systems described by singularly perturbed equations of the type $x''+x+\epsilon f(x,x')=0$. By performing a perturbative calculation based on normal…
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented.…
A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent…
We introduce a scalar reduction method for forced or coupled systems with nonlinearities in both heterogeneity and coupling strength. Heterogeneity is formulated as a relatively weak but nonlinear alteration of the vector field(s). The…
Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…