Related papers: Unifying Lyapunov exponents with probabilistic unc…

The statistical properties of finite-time Lyapunov exponents at the Ulam point of the logistic map are investigated. The exact analytical expression for the autocorrelation function of one-step Lyapunov exponents is obtained, allowing the…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…

In this technical communique, we generalize the well-known Lyapunov-based stabilizability and detectability tests for discrete-time linear time-invariant systems to polytopic linear parameter-varying systems using the class of so-called…

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,…

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…

In order to study the chaotic behavior of a system with non-local interactions, we will consider weakly coupled non-commutative field theories. We compute the Lyapunov exponent of this exponential growth in the large Moyal-scale limit to…

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…

Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…

Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional test for chaos using the maximal Lyapunov exponent.…

This paper discusses stability and robustness properties of a recently proposed observer algorithm for linear time varying systems. The observer is based on the approximation and subsequent modification of the non-negative Lyapunov…

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…

We study how spatiotemporal chaos in dynamical systems can be controlled by stochastically returning them to their initial conditions. Focusing on discrete nonlinear maps, we analyze how key measures of chaos -- the Lyapunov exponent and…

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 study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are…

Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…

This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian L\'evy noise. In a suitable moving frame, the linearisation of such a system can be regarded as a small perturbation of a…

This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…