Related papers: Time-oscillating Lyapunov modes and auto-correlati…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
Finite-time Lyapunov exponents and vectors are used to define and diagnose boundary-layer type, two-timescale behavior in the tangent linear dynamics and to determine the associated manifold structure in the flow of a finite-dimensional…
We introduce a definition of a "localization width" whose logarithm is given by the entropy of the distribution of particle component amplitudes in the Lyapunov vector. Different types of localization widths are observed, for example, a…
Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov…
Numerical integrations of the Solar System reveal a remarkable stability of the orbits of the inner planets over billions of years, in spite of their chaotic variations characterized by a Lyapunov time of only 5 million years and the lack…
Two important classes of spatio-temporal patterns, namely, spatio-temporal chaos and self-replicating patterns, for a representative three variable autocatalytic reaction mechanism coupled with diffusion has been studied. The…
Using direct numerical simulation we study the behavior of the maximal Lyapunov exponent in thin-layer turbulence, where one dimension of the system is constrained geometrically. Such systems are known to exhibit transitions from fully…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
We consider the covariant Lyapunov vectors (CLV) of a high-dimensional Hamiltonian flow in the case of long range potential, namely the Hamiltonian Mean Field (HMF) problem, by studying the behavior of the Lyapunov spectra and the…
This work provides an experimental method for simultaneously measuring finite time Lyapunov exponent fields for multiple particle groups, including non-flow tracers, in three-dimensional multiphase flows. From sequences of particle images,…
Time-irreversibility is a distinctive feature of non-equilibrium dynamics and several measures of irreversibility have been introduced to assess the distance from thermal equilibrium of a stochastically driven system. While the dynamical…
A method for constructing homogeneous Lyapunov functions of degree 1 from polynomial invariant sets is presented for linear time varying systems, homogeneous dynamic systems and the class of nonlinear systems that can be represented as…
Boundary time crystals exhibit spontaneous breaking of continuous time-translation symmetry through persistent periodic oscillations in driven-dissipative many-body systems. Here, we show that multilevel interference provides a natural…
This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…
We present an index for the local sensitivity of spatiotemporal structures in coupled oscillatory systems based on the asymptotic scaling of local-in-space, finite-time Lyapunov Exponents. For a system of nonlocally-coupled R\"{o}ssler…
The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease…
We study the implications of translation invariance on the tangent dynamics of extended dynamical systems, within a random matrix approximation. In a model system, we show the existence of hydrodynamic modes in the slowly growing part of…
We conduct direct numerical simulations to investigate the synchronization of Kolmogorov flows in a periodic box, with a focus on the mechanisms underlying the asymptotic evolution of infinitesimal velocity perturbations, also known as…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…