Related papers: Analysis of Round Off Errors with Reversibility Te…
We study the existence of asymptotically stable periodic trajectories induced by reset feedback. The analysis is developed for a planar system. Casting the problem into the hybrid setting, we show that a periodic orbit arises from the…
This paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. Three approaches are examined: residual assessment, the method of modified equations, and…
We present a new method for generating robust guesses for unstable periodic orbits (UPOs) by post-processing turbulent data using dynamic mode decomposition (DMD). The approach relies on the identification of near-neutral, repeated…
This work considers reversed evolution in dynamical systems. In particular, asymptotic behavior of chaotic systems, when their orbits evolve backwards in time. Reversed dynamics reveals important aspects of the trajectories, such as a new…
We deal with the orbit determination problem for hyperbolic maps. The problem consists in determining the initial conditions of an orbit and, eventually, other parameters of the model from some observations. We study the behaviour of the…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
Steady state fluctuation relations for dynamical systems are commonly derived under the assumption of some form of time-reversibility and of chaos. There are, however, cases in which they are observed to hold even if the usual notion of…
The paper algorithmizes the problem of regime change point identification for data measured in a system exhibiting impulsive behaviors. This is a fundamental challenge for annotation of measurement data relevant, e.g., for designing…
A method to quantify robust performance for situations where structured parameter variations and initial state errors rather than extraneous disturbances are the main performance limiting factors is presented. The approach is based on the…
Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We…
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…
The out-of-time ordered correlator (OTOC) is a measure of scrambling of quantum information. Scrambling is intuitively considered to be a significant feature of chaotic systems and thus the OTOC is widely used as a measure of chaos. For…
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of…
In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set $X$ allows us to describe precisely the behaviour of such systems. We can predict by means of closed…
The reader can find in the literature a lot of different techniques to study the dynamics of a given system and also, many suitable numerical integrators to compute them. Notwithstanding the recent work of Maffione et al. (2011a) for…
We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…
We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour…
A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model…
We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular,…
Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded…