Related papers: On the relation between reliable computation time,…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…
Fast scrambling, quantified by the exponential initial growth of Out-of-Time-Ordered-Correlators (OTOCs), is the ability to efficiently spread quantum correlations among the degrees of freedom of interacting systems, and constitutes a…
The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with…
The exponential growth or decay with time of the out-of-time-order commutator (OTOC) is one widely used diagnostic of many-body chaos in spatially-extended systems. In studies of many-body classical chaos, it has been noted that one can…
Stability margins for linear time-varying (LTV) and switched-linear systems are traditionally computed via quadratic Lyapunov functions, and these functions certify the stability of the system under study. In this work, we show how the more…
We show that any solution of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent Riemannian metric.
The concept of environmental interface is defined and analyzed from the point of view of the possible source of non-standard behaviour. The energy balance equation is written for the interface where all kinds of energy transfer occur. It is…
We compute the full Lyapunov spectra for a hard-disk fluid under temperature gradient and shear. The system is thermalized by deterministic and time-reversible scattering at the boundary. This thermostating mechanism allows for energy…
This works investigates the Lyapunov-Oseledets spectrum of transfer operator cocycles associated to one-dimensional random paired tent maps depending on a parameter $\epsilon$, quantifying the strength of the \emph{leakage} between two…
This paper considers the problem of finite-time stability for stochastic nonlinear systems. A new Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing…
The reliable computation time (RCT, marked as Tc) when applying a double precision computation of a variable parameters logistic map (VPLM) is studied. First, using the method proposed, the reliable solutions for the logistic map are…
This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both…
In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov…
In this paper, we develop a systematic method for constructing a generalized discrete-time control Lyapunov function for the flexible-step Model Predictive Control (MPC) scheme, recently introduced in [2], when restricted to the class of…
Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate…
We conjecture a chaos energy bound, an upper bound on the energy dependence of the Lyapunov exponent for any classical/quantum Hamiltonian mechanics and field theories. The conjecture states that the Lyapunov exponent $\lambda(E)$ grows no…
This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some…
Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time -- the most clear example being the Solar System -- but the situation for their quantum counterparts is less well understood. As a…
We discuss the behavior of the largest Lyapunov exponent $\lambda$ in the incoherent phase of large ensembles of heterogeneous, globally-coupled, phase oscillators. We show that the scaling with the system size $N$ depends on the details of…