In 1892, the general problem of stability by the first approximation was considered by Lyapunov. He proved that if the system of the first approximation is regular and all its Lyapunov exponents (or characteristic exponents) are negative, then the solution of the original system is asymptotically Lyapunov stable. In 1930, it was stated by O. Perron that the requirement of regularity of the firs...

We present a fast, simple matrix method of computing the unique invariant measure and associated Lyapunov exponents of a nonlinear iterated function system. Analytic bounds for the error in our approximate invariant measure (in terms of the Hutchinson metric) are provided, while convergence of the Lyapunov exponent estimates to the true value is assured. As a special case, we are able to rigoro...

The purpose of this paper is to show how the stability properties of non-linear dynamic models may be characterized, where the degree of stability is deÞned by the effects of exogenous shocks on the evolution of the observed stochastic system. Smoothed Lyapunov exponents are a generalization of Lyapunov exponents for deterministic systems. We argue that smoothed Lyapunov exponents can be used t...

in this paper, we discuss the dynamical properties of a chemical reactor model including lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. we study the synchronization of chemical reactors model via sliding mode control scheme. the stability of proposed method is proved by barbalate’s lemma. numeri...

Two important classes of spatio-temporal patterns, namely, spatiotemporal chaos and self-replicating patterns, for a representative three variable autocatalytic reaction mechanism coupled with diffusion has been studied. The characterization of these patterns has been carried out in terms of Lyapunov exponents and dimension density. The results show a linear scaling as a function of sub-system ...

BACKGROUND/AIM Pneumocardiography (PNCG) is the recording method of cardiac-induced tracheal air flow and pressure pulsations in the respiratory airways. PNCG signals reflect both the lung and heart actions and could be accurately recorded in spontaneously breathing anesthetized rats. Nonlinear analysis methods, including the Lyapunov exponent, can be used to explain the biological dynamics of ...

We consider the quasi-periodic cocycles (ω, A(x, E)) : (x, v) 7→ (x+ω, A(x, E)v) with ω Diophantine. Let M2(C) be a normed space endowed with the matrix norm, whose elements are the 2 × 2 matrices. Assume that A : T × E → M2(C) is jointly continuous, depends analytically on x ∈ T and is Hölder continuous in E ∈ E , where E is a compact metric space and T is the torus. We prove that if two Lyapu...

We show that the integrated Lyapunov exponents of C volume preserving diffeomorphisms are simultaneously continuous at a given diffeomorphism only if the corresponding Oseledets splitting is trivial (all Lyapunov exponents equal to zero) or else dominated (uniform hyperbolicity in the projective bundle) almost everywhere. We deduce a sharp dichotomy for generic volume preserving diffeomorphisms...

Lyapunov exponents represent important quantities to characterize the properties of dynamical systems. We show that the Lyapunov exponents of two di€erent dynamical systems that can be converted to each other by a transformation of variables are identical. Moreover, we derive sucient conditions on the transformation for this invariance property to hold. In particular, it turns out that the tra...