Related papers: Invariance of Lyapunov exponents and Lyapunov dime…
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,…
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…
The Lyapunov rank of a cone is the dimension of the Lie algebra of its automorphism group. It is invariant under linear isomorphism and in general not unique - two or more non-isomorphic cones can share the same Lyapunov rank. It is…
In this paper we analyze local structure of several chaotic attractors recently suggested in literature as pseudohyperbolic. The absence of tangencies and thus the presence of the pseudohyperbolicity is verified using the method of angles…
We study the singular values and Lyapunov exponents of non-stationary random matrix products subject to small, absolutely continuous, additive noise. Consider a fixed sequence of matrices of bounded norm. Independently perturb the matrices…
The exact value of the Lyapunov exponents for the random matrix product $P_N = A_N A_{N-1}...A_1$ with each $A_i = \Sigma^{1/2} G_i^{\rm c}$, where $\Sigma$ is a fixed $d \times d$ positive definite matrix and $G_i^{\rm c}$ a $d \times d$…
This paper is devoted to provide some new results on Lyapunov type inequalities for the periodic boundary value problem at higher eigenvalues. Our main result is derived from a detailed analysis on the number and distribution of zeros of…
We consider orthogonally invariant probability measures on $\mathrm{GL}_n(\mathbb{R})$ and compare the mean of the logs of the moduli of eigenvalues of the matrices to the Lyapunov exponents of random matrix products independently drawn…
We consider linear cocycles over non-uniformly hyperbolic dynamical systems. The base system is a diffeomorphism $f$ of a compact manifold $X$ preserving a hyperbolic ergodic probability measure $\mu$. The cocycle $A$ over $f$ is Holder…
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…
Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…
The cloned dynamical system theory is introduced and the Lyapunov exponents of this system are qualitatively proven to be same as the original dynamical system. This property indicates that these two systems have the same error propagation…
An alternative characterization of Minkowski--Lyapunov functions is derived. The derived characterization enables a computationally efficient utilization of Minkowski--Lyapunov functions in arbitrary finite dimensions. Due to intrinsic…
The multiple parameter logistic equation has previously been utilized to determine the global stability of ternary codes, based on the arrangement of different symbols within the code. This approach has been extended to DNA and RNA…
We discuss the role played by the Lyapunov exponents in the dynamics of Zhang's model of Self-Organized Criticality. We show that a large part of the spectrum (slowest modes) is associated with the energy transpor in the lattice. In…
We study random dynamical systems generated by volume-preserving piecewise $C^{1}$ maps. For this class of systems, we establish an invariance principle stating that if all Lyapunov exponents vanish, then there exists a measurable family of…
I propose that stiffness may be defined and quantified for nonlinear systems using Lyapunov exponents, and demonstrate the relationship that exists between stiffness and the fractal dimension of a strange attractor: that stiff chaos is thin…
The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
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.