相关论文: Applying the DFT representation for describing the…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their…
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…
We use finite-time Lyapunov exponent (FTLE) distributions to probe transition mechanisms in high-dimensional reservoir maps trained on low-dimensional chaotic dynamics across multiple regimes. While trained reservoirs accurately predict…
Discrete fractional order chaotic systems extends the memory capability to capture the discrete nature of physical systems. In this research, the memristive discrete fractional order chaotic system is introduced. The dynamics of the system…
The quantitative determination of the order-chaos transition in a nonlinear dynamical system described by H\'enon mapping defined as $x[n+1]=1.0-A*x[n]^2+B*y[n], y[n+1]=B*x[n]$, where $B=0.3$, and $A$ is an adjustable control parameter, was…
This paper is devoted to show the results obtained by using the magnitude-squared coherence for determining order-chaos transition in a system described by the logistic equation dynamics. For determining the power spectral density of a…
When chaotic signals are used in practical communication systems, it is essential to control and eventually limit the spectral bandwidth occupied by these signals. One way to achieve this goal is to insert a discrete-time filter into a…
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
In this paper, we use Lyapunov exponents to analyze how the dynamical properties of the H\'enon map change as a function of the coefficients of a linear filter inserted in its feedback loop. We show that the generated orbits can be chaotic…
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 consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
In this Letter we show that the analysis of Lyapunov-exponents fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a Gaussian approximation for the large deviation function that…
The dependence of the Lyapunov exponent on the closeness parameter, $\epsilon$, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we…
Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov…
The parametric instability contribution to the largest Lyapunov exponent (LLE) is derived for a mean-field Hamiltonian model, with attractive long-range interactions. This uses a recent Riemannian approach to describe Hamiltonian chaos with…
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…
Density functional theory (DFT) provides a theoretical framework for efficient and fairly accurate calculations of the electronic structure of molecules and crystals. The main features of density functional theory are described and DFT…
Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…
Using direct numerical simulation we study the behavior of the maximal Lyapunov exponent in thin-layer turbulence, where one dimension of the system is constrained geometrically. Such systems are known to exhibit transitions from fully…