相关论文: Global analysis of a continuum model for monotone …

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…

We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective…

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the…

The present work analyzes the statistics of finite scale local Lyapunov exponents of pairs of fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully developed…

Coupled arrays of Andronov-Hopf oscillators are investigated. These arrays can be diffusively or repulsively coupled, and can serve as central pattern generator models in animal locomotion and robotics. It is shown that repulsive coupling…

We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting…

In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further…

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…

We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The…

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that…

We consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we…

We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.

The collective behavior of biological oscillators has been recognized as an important problem for several decades, but its control has come into limelight only recently. Much of the focus for control has been on desynchronization of an…

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as…

The present work analyzes the distribution function of the finite scale local Lyapunov exponent of a pair fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully…

We study the nonlinear dynamics of globally coupled nonidentical oscillators in the framework of two order parameter (mean field and amplitude-frequency correlator) reduction. The main result of the paper is the exact solution of the…

A generalized Lyapunov method is outlined which predicts global stability of a broad class of dissipative dynamical systems. The method is applied to the complex Lorenz model and to the Navier-Stokes equations. In both cases one finds…

In this paper, we show that under a generic condition of the coefficient of a stochastic phase oscillator the Lyapunov exponent of the linearization along an arbitrary solution is always negative. Consequently, the generated random…

The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g. mean field models) or inactive (e.g…

Clock synchronization is a widely discussed topic in the engineering literature. Ensuring that individual clocks are closely aligned is important in network systems, since the correct timing of various events in a network is usually…