Related papers: Structural Stability and Hyperbolicity Violation i…
In this paper we consider the problem of determining the stability properties, and in particular assessing the exponential stability, of a singularly perturbed linear switching system. One of the challenges of this problem arises from the…
The evolution of the scale parameter in the Hu-Sawicki model is examined. We search the parameter area for instabilities. It turns out the parameter area of physically meaningful evolution is non-existent. For greater stability a…
Localization of acoustic waves in a one dimensional water duct containing many randomly distributed air filled blocks is studied. Both the Lyapunov exponent and its variance are computed. Their statistical properties are also explored…
We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…
The topological structure of basin boundaries plays a fundamental role in the sensitivity to the initial conditions in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian…
"Sticky" motion in mixed phase space of conservative systems is difficult to detect and to characterize, in particular for high dimensional phase spaces. Its effect on quasi-regular motion is quantified here with four different measures,…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
We prove that small nonlinear perturbations of random linear dynamics admitting a tempered exponential dichotomy have a random version of the shadowing property. As a consequence, if the exponential dichotomy is uniform, we get that the…
There are recent shifts in demand for design controllers from simplified to complex model-based. Although simplification approaches are successful in many areas of engineering control systems, high-fidelity simulation-based control design,…
We perform direct numerical simulation of the incompressible Navier-Stokes equation with forcing at different spatial dimensions and measure turbulent and chaotic properties. Lyapunov exponents, $\lambda$, decrease with dimension, and…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
The predictability of weather and climate is strongly state-dependent: special and extremely relevant atmospheric states like blockings are associated with anomalous instability. Indeed, typically, the instability of a chaotic dynamical…
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…
This work investigates the stability properties of Lyapunov exponents of transfer operator cocycles from a measure-theoretic perspective. Our results focus on so-called Blaschke product cocycles, a class of random dynamical systems amenable…
Using examples we test formulae previously conjectured to give the fractal information dimension of chaotic repellors and their stable and unstable manifolds in ``typical'' dynamical systems in terms of the Lyapunov exponents and the…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
In this paper, we introduce the unstable topological pressure for C^1-smooth partially hyperbolic diffeomorphisms with sub-additive potentials. Moreover, without any additional assumption, we have established the expected variational…
A detailed analysis of conditions on 2-body interaction potential, which ensure stability, superstability or strong superstability of statistical systems is given. There has been given the connection between conditions of superstability…