Related papers: From synchronization to Lyapunov exponents and bac…
This is a survey of known results on estimating the principal Lyapunov exponent of a time-dependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of…
Auxiliary system approach and various nearest neighbor methods are widely used to detect generalized synchronization in non-identical coupled systems. These methods generally give contradictory results. Therefore one method alone is not…
This paper presents a distributed Lyapunov-based control framework for achieving both complete and phase synchronization in a class of leader-follower multi-agent systems composed of identical chaotic agents. The proposed approach…
Finite-time Lyapunov exponents and vectors are used to define and diagnose boundary-layer type, two-timescale behavior in the tangent linear dynamics and to determine the associated manifold structure in the flow of a finite-dimensional…
The phase space trajectories of many body systems charateristic of simple fluids are highly unstable. We quantify this instability by a set of Lyapunov exponents, which are the rates of exponential divergence, or convergence, of initial…
We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupled models, the stability results obtained in the continuum limit are…
The Lyapunov exponents of a dynamical system measure the average rate of exponential stretching along an orbit. Positive exponents are often taken as a defining characteristic of chaotic dynamics. However, the standard…
Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate…
We show the first solvable chaotic synchronization model of unidirectionally coupled dynamical systems. We establish a new interpretation of the conditional Lyapunov exponent that characterizes chaotic synchronization completely. Moreover,…
First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and…
New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…
We have found a synchronization behavior between two identical chaotic systems^M when their delay times are modulated by a common irregular signal. ^M This phenomenon is demonstrated both in two identical chaotic maps whose delay times are…
We investigate the characteristics of temporal phase locking states observed in the route to phase synchronization. It is found that before phase synchronization there is a periodic phase synchronization state characterized by periodic…
This paper presents some new criteria for partial exponential stability of a slow-fast nonlinear system with a fast scalar variable using periodic averaging methods. Unlike classical averaging techniques, we construct an averaged system by…
Instabilities in 1D spatially extended systems are studied with the aid of both temporal and spatial Lyapunov exponents. A suitable representation of the spectra allows a compact description of all the possible disturbances in tangent…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
We introduce a novel concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset…
We investigate a transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces. We analyze the synchronization phenomenon in the ensemble of particles moving with friction in…
In the dynamical systems approach to describing turbulent or otherwise chaotic flows, an important quantity is the Lyapunov exponents and vectors that characterize the strange attractor of the flow. In particular, knowledge of the Lyapunov…
The problem of synchronization of coupled self-oscillators by external force is studied. The charts of Lyapunov's exponents in the "frequency - amplitude" parameter plane are obtained within the framework of the phase approximation. We…