Related papers: Estimates for principal Lyapunov exponents: A surv…
Linear nonautonomous/random parabolic partial differential equations are considered under the Dirichlet, Neumann or Robin boundary conditions, where both the zero order coefficients in the equation and the coefficients in the boundary…
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…
For cooperative random linear systems of ordinary differential equations a method is presented of obtaining lower estimates of the top Lyapunov exponent. The proofs are based on applying some polynomial Lyapunov-like function. Known…
Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…
We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…
We discuss several numerical methods for calculating Lyapunov exponents (a quantitative measure of chaos) in systems of ordinary differential equations. We pay particular attention to constrained systems, and we introduce a variety of…
A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in…
We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of…
The problem of evaluation of Lyapunov exponent in queueing network analysis is considered based on models and methods of idempotent algebra. General existence conditions for Lyapunov exponent to exist in generalized linear stochastic…
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…
We revisit the canonical continuous-time and discrete-time matrix algebraic and matrix differential equations that play a central role in Lyapunov based stability arguments. The goal is to generalize and extend these types of equations and…
An integral formula is given representing the generalized principal Lyapunov estimate for random linear parabolic PDEs. As an application, an upper estimate of the exponent is obtained.
Generic dynamical systems have `typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system has also trajectories with exceptional values of the exponents, corresponding to…
A simple example that I have been requested illustrates the statement in E-print nlin.CD/0201060 that solutions of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent…
According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…
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…
The problem of analytical estimation of the Lyapunov exponents and Lyapunov timescales of the motion in multiplets of interacting nonlinear resonances is considered. To this end, we elaborate a unified framework, based on the separatrix map…
Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.
This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some…
The goal of this paper is twofold. In the first part we discuss a general approach to determine Lyapunov exponents from ensemble- rather than time-averages. The approach passes through the identification of locally stable and unstable…