Related papers: Recent Advances in Coupled Oscillator Theory
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
We consider a confining Yang-Mills theory without Goldstone Bosons which could describe the bosonic sector of the weak interactions. This model can be gauge invariantly regularized on a lattice. A strong coupling analysis of the low lying…
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…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances raises the question how these models relate to each other. In particular it is hard to distinguish between…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
We consider the Saintillan--Shelley kinetic model of active rodlike particles in Stokes flow (Saintillan & Shelley 2008a,b), for which the uniform, isotropic suspension of pusher particles is known to be unstable in certain settings.…
Synchronization processes in populations of identical networked oscillators are in the focus of intense studies in physical, biological, technological and social systems. Here we analyze the stability of the synchronization of a network of…
We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered.…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
We investigate the influence that adding a new coupling has on the linear stability of the synchronous state in coupled oscillators networks. Using a simple model we show that, depending on its location, the new coupling can lead to…
We show that a wide class of uncoupled limit cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven…
We show that peculiar collective dynamics called slow switching arises in a population of leaky integrate-and-fire oscillators with delayed, all-to-all pulse-couplings. By considering the stability of cluster states and symmetry possessed…
Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with…
We consider a system of three interacting van der Pol oscillators with reactive coupling. Phase equations are derived, using proper order of expansion over the coupling parameter. The dynamics of the system is studied by means of the…
Weakly coupled limit cycle oscillators can be reduced into a system of weakly coupled phase models. These phase models are helpful to analyze the synchronization phenomena. For example, a phase model of two oscillators has a one-dimensional…
A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nano-particles. In the case of monovalent ions, we derive a weak-coupling…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…