Related papers: From synchronization to Lyapunov exponents and bac…
We present stability and recurrence results for a class of stochastic hybrid dynamical systems with oscillating flow maps. These results are developed by introducing averaging tools that parallel those already existing for ordinary…
In this technical communique, we generalize the well-known Lyapunov-based stabilizability and detectability tests for discrete-time linear time-invariant systems to polytopic linear parameter-varying systems using the class of so-called…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
The conditions for synchronization in unidirectionally coupled chaotic oscillators are revisited. We demonstrate with typical examples that the conditional Lyapunov exponents (CLEs) play an important role in distinguishing between…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering has been introduced for the periodic Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the nonlinear…
We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual…
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 the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On…
The problem of formulating self-consistent local and global stability exponents is shown to require global separation of variables. Posing the separation of variable problem, we see that many such separations are possible, but only one is…
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…
An analytic quasi-periodic cocycle is a linear cocycle over a fixed ergodic torus translation of one or several variables, where the fiber action depends analytically on the base point. Consider the space of all such cocycles of any given…
The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…
We derive asymptotic estimates for the projection of the vorticity onto principal directions of material stretching in 3D flows. In flows with pointwise bounded vorticity, these estimates predict vorticity alignment with Lyapunov vectors…
In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…
We consider a stochastic partial differential equation close to bifurcation of pitchfork type, where a one-dimensional space changes its stability. For finite-time Lyapunov exponents we characterize regions depending on the distance from…
We study the influence of telegraph noise on synchrony of limit cycle oscillators. Adopting the phase description for these oscillators, we derive the explicit expression for the Lyapunov exponent. We show that either for weak noise or…
This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…