Related papers: Estimating the Largest Lyapunov Exponent Based on …
A general indicator of the presence of chaos in a dynamical system is the largest Lyapunov exponent. This quantity provides a measure of the mean exponential rate of divergence of nearby orbits. In this paper, we show that the so-called…
In this paper, we discuss the Lyapunov exponent definition of chaos and how it can be used to quantify the chaotic behavior of a system. We derive a way to practically calculate the Lyapunov exponent of a one-dimensional system and use it…
Chaotic systems have been investigated in the most diverse areas. One of the first steps in chaotic system research is the detection of chaos. The largest Lyapunov exponent (LLE) is one of the most widely used techniques for this purpose.…
Lyapunov exponents measure the average exponential growth rate of typical linear perturbations in a chaotic system, and the inverse of the largest exponent is a measure of the time horizon over which the evolution of the system can be…
We explicitly compute the maximal Lyapunov exponent for a switched system on $\mathrm{SL}_2(\mathbb R)$. This computation is reduced to the characterization of optimal trajectories for an optimal control problem on the Lie group.
This paper investigates the behaviour of open billiard systems in high-dimensional spaces. Specifically, we estimate the largest Lyapunov exponent, which quantifies the rate of divergence between nearby trajectories in a dynamical system.…
We calculate analytically the largest Lyapunov exponent of the so-called $\alpha XY$ Hamiltonian in the high energy regime. This system consists of a $d$-dimensional lattice of classical spins with interactions that decay with distance…
The conditional Lyapunov exponent is defined for investigating chaotic synchronization, in particular complete synchronization and generalized synchronization. We find that the conditional Lyapunov exponent is expressed as a formula in…
In the current work we demonstrate the principal possibility of prediction of the response of the largest Lyapunov exponent of a chaotic dynamical system to a small constant forcing perturbation via a linearized relation, which is computed…
Dynamics of driven dissipative Frenkel-Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of the system in the presence of external forces…
We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for…
The largest Lyapunov exponent $\lambda^+$ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions.…
In this work we present a theoretical and numerical study of the behaviour of the maximum Lyapunov exponent for a generic coupled-map-lattice in the weak-coupling regime. We explain the observed results by introducing a suitable…
The maximum Lyapunov exponent (referred to the mean half-period of phase libration) of the motion in the chaotic layer of a nonlinear resonance subject to symmetric periodic perturbation, in the limit of infinitely high frequency of the…
We present a general formalism for computing the largest Lyapunov exponent and its fluctuations in spatially extended systems described by diffusive fluctuating hydrodynamics, thus extending the concepts of dynamical system theory to a…
Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…
Synchronization of chaotic system may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, {\bf 56},…
The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with…
Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with the imperfect measurement of initial conditions. Finite-time estimates of the exponent, however,…
The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent…