相关论文: Evaluation of Lyapunov exponent in generalized lin…
We consider generalized linear stochastic dynamical systems with second-order state transition matrices. The entries of the matrix are assumed to be either independent and exponentially distributed or equal to zero. We give an overview of…
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…
By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network, and construct a measure to estimate the network Maximum Lyapunov Exponent (nMLE)…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
This is a survey of known results on estimating the principal Lyapunov exponent of a time-dependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of…
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…
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…
Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the…
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…
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we…
We consider (max,+)-algebra products of random matrices, which arise from performance evaluation of acyclic fork-join queueing networks. A new algebraic technique to examine properties of the product and investigate its limiting behaviour…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to trajectories that stay within a bounded domain for asymptotically long times. This is motivated by the desire to characterize local dynamical…
According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…
We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in…
Generic dynamical systems have `typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system has also trajectories with exceptional values of the exponents, corresponding to…
We discuss certain recent metric space methods and some of the possibilities these methods provide, with special focus on various generalizations of Lyapunov exponents originally appearing in the theory of dynamical systems and differential…
The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…
The goal of this paper is twofold. In the first part we discuss a general approach to determine Lyapunov exponents from ensemble- rather than time-averages. The approach passes through the identification of locally stable and unstable…
It is well-known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose an alternative definition of Lyapunov exponent in terms of Lipschitz maps, which are not necessarily differentiable. We show…