Related papers: Important Notes on Lyapunov Exponents
Lyapunov exponents are indicators for the chaotic properties of a classical dynamical system. They are most naturally defined in terms of the time evolution of a set of so-called covariant vectors, co-moving with the linearized flow in…
Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.
We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors…
We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schr\"odinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose…
This paper is devoted to study stability of Lyapunov exponents and simplicity of Lyapunov spectrum for bounded random compact operators on a separable infinite-dimensional Hilbert space from a generic point of view generated by the…
There are presented examples of the rather sudden and violent explosion of the strange attractor of a one-dimensional driven damped anharmonic oscillator induced by a relatively small change of the amplitude of the strongly nonperturbative…
This study introduces a modified quadratic Lorenz attractor. The properties of this new chaotic system are analysed and discussed in detail, by determining the equilibria points, the eigenvalues of the Jacobian, and the Lyapunov exponents.…
In this paper, we give a quantitative estimate for the sum of the first $N$ Lyapunov exponents for random perturbations of a natural class $2N$-dimensional volume-preserving systems exhibiting strong hyperbolicity on a large but…
In this paper, we study the problem of state observation of nonlinear systems over an erasure channel. The notion of mean square exponential stability is used to analyze the stability property of observer error dynamics. The main results of…
It was shown that quantum analysis constitutes the proper analytic basis for quantization of Lyapunov exponents in the Heisenberg picture. Differences among various quantizations of Lyapunov exponents are clarified.
We find some bounds for the internal radii of stable and unstable manifolds of points in terms of their Lyapunov exponents under the assumption of the existence of a dominated splitting.
This paper presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis of the input to state stability property,…
Two approaches are presented for computing upper bounds on Lyapunov exponents and their sums, and on the Lyapunov dimension, among all trajectories of a dynamical system governed by ordinary differential equations. The first approach…
We prove that for any holomorphic map, and any bounded orbit which does not accumulate to a singular set or to an attracting cycle, its lower Lyapunov exponent is non-negative. The same result holds for unbounded orbits, for maps with a…
This work is devoted to further consideration of the Henon map with negative values of the shrinking parameter and the study of transient oscillations, multistability, and possible existence of hidden attractors. The computation of the…
In this paper we give sufficient conditions for random splitting systems to have a positive top Lyapunov exponent. We verify these conditions for random splittings of two fluid models: the conservative Lorenz-96 equations and Galerkin…
Delay differential equations (DDEs) are infinite-dimensional systems, so even a scalar, unforced nonlinear DDE can exhibit chaos. Lyapunov exponents are indicators of chaos and can be computed by comparing the evolution of infinitesimally…
Consider a $C^1$ vector field together with an ergodic invariant probability that has $\ell$ nonzero Lyapunov exponents. Using orthonormal moving frames along certain transitive orbits we construct a linear system of $\ell$ differential…
We report a numerical investigation of the fluctuations of the Lyapunov exponent of a two dimensional non-interacting disordered system. While the ratio of the mean to the variance of the Lyapunov exponent is not constant, as it is in one…
This work contains the results from a comprehensive study of a new class of attractors. The attractors in this class are characterized by strong local instability, but they are not uniformly hyperbolic. Rigorous results on their dynamical,…