Statistics of finite-time Lyapunov exponents in a random time-dependent potential.
نویسندگان
چکیده
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 chaotic dynamics, lambda tends to a unique value (the usual Lyapunov exponent lambda(infinity)) for almost all trajectories as t is sent to infinity, but for finite t it depends on the initial conditions of the trajectory and can be considered as a statistical quantity. We compute for a particle moving in a randomly time-dependent, one-dimensional potential how the distribution function P(lambda;t) approaches the limiting distribution P(lambda; infinity)=delta(lambda-lambda(infinity)). Our method also applies to the tail of the distribution, which determines the growth rates of moments of M(ij). The results are also applicable to the problem of wave-function localization in a disordered one-dimensional potential.
منابع مشابه
Finite time stabilization of time-delay nonlinear systems with uncertainty and time-varying delay
In this paper, the problem of finite-time stability and finite-time stabilization for a specific class of dynamical systems with nonlinear functions in the presence time-varying delay and norm-bounded uncertainty terms is investigated. Nonlinear functions are considered to satisfy the Lipchitz conditions. At first, sufficient conditions to guarantee the finite-time stability for time-delay nonl...
متن کاملOn Entropy and Lyapunov Exponents for Finite-State Channels
The Finite-State Markov Channel (FSMC) is a time-varying channel having states that are characterized by a finite-state Markov chain. These channels have infinite memory, which complicates their capacity analysis. We develop a new method to characterize the capacity of these channels based on Lyapunov exponents. Specifically, we show that the input, output, and conditional entropies for this ch...
متن کاملOn the Scaling Function of Lyapunov Exponents for Intermittent Maps
The scaling function of Lyapunov exponents for intermittent systems is full of particularities if compared with hyperbolic cases or the usual, nonhyperbolic, parabola. One particularity arises when this function is calculated from finite-time Lyapunov exponents: Different scaling properties with respect to the length of the finite-time chains emerge. As expected from random walk models, the sca...
متن کاملModel Based Method for Determining the Minimum Embedding Dimension from Solar Activity Chaotic Time Series
Predicting future behavior of chaotic time series system is a challenging area in the literature of nonlinear systems. The prediction's accuracy of chaotic time series is extremely dependent on the model and the learning algorithm. On the other hand the cyclic solar activity as one of the natural chaotic systems has significant effects on earth, climate, satellites and space missions. Several m...
متن کاملFinite time blow up of solutions of the Kirchhoff-type equation with variable exponents
In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 66 6 Pt 2 شماره
صفحات -
تاریخ انتشار 2002