Related papers: Computation of the largest Lyapunov exponent using…
Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…
We consider three matrix models of order 2 with one random entry $\epsilon$ and the other three entries being deterministic. In the first model, we let $\epsilon\sim\textrm{Bernoulli}\left(\frac{1}{2}\right)$. For this model we develop a…
We describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic. (This is an alternative to the usual approach of computing the largest Lyapunov exponent.) Our method is a 0-1 test for chaos…
A new order parameter approximation to Random Boolean Networks (RBN) is introduced, based on the concept of Boolean derivative. A statistical argument involving an annealed approximation is used, allowing to measure the order parameter in…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…
The effective numerical method is developed performing the test of the hyperbolicity of chaotic dynamics. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a…
We consider a general class of maps of the interval having Lyapunov subexponential instability $|\delta x_{t}|\sim|\delta x_{0}|\exp[\Lambda_{t}(x_{0})\zeta(t)]$, where $\zeta(t)$ grows sublinearly as $t\rightarrow\infty$. We outline here a…
We investigate finite-time Lyapunov exponents (FTLEs), a measure for exponential separation of input perturbations, of deep neural networks within the framework of continuous-depth neural ODEs. We demonstrate that FTLEs are powerful…
Covariant Lyapunov vectors characterize the directions along which perturbations in dynamical systems grow. They have also been studied as predictors of critical transitions and extreme events. For many applications like, for example,…
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT$_2$ at large central charge c. The Lyapunov exponent $\lambda_L$, which is a diagnostic for the early onset of chaos, receives $1/c$ corrections that may be…
By performing a large number of fully resolved simulations of incompressible homogeneous and isotropic two dimensional turbulence, we study the scaling behavior of the maximal Lyapunov exponent, the Kolmogorov-Sinai entropy and attractor…
Identification of the unknown parameters and orders of fractional chaotic systems is of vital significance in controlling and synchronization of fractional-order chaotic systems. However there exist basic hypotheses in traditional…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values…
Lyapunov functions play a fundamental role in analyzing the stability and convergence properties of optimization methods. In this paper, we propose a novel and straightforward approach for constructing Lyapunov functions for first-order…
A chaotic system is a highly volatile system characterized by its sensitive dependence on initial conditions and outside factors. Chaotic systems are prevalent throughout the world today: in weather patterns, disease outbreaks, and even…
A method to estimate Lyapunov spectra from spatio-temporal data is presented, which is well-suited to be applied to experimental situations. It allows to characterize the high-dimensional chaotic states, with possibly a large number of…
In this paper we introduce the fractional-order variant of a Gompertz-like discrete system. The chaotic behavior is suppressed with an impulsive control algorithm. The numerical integration and the Lyapunov exponent are obtained by means of…
We compute Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in delay-differential equations with large time delay. We find that characteristic LVs, and backward (Gram-Schmidt) LVs, exhibit long-range correlations,…
We discuss the effects of finite perturbations in fully developed turbulence by introducing a measure of the chaoticity degree associated to a given scale of the velocity field. This allows one to determine the predictability time for…