Related papers: Records and occupation time statistics for area-pr…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
It was conjectured recently that Statiscally Preserved Structures underlie the statistical physics of turbulent transport processes. We analyze here in detail the time-dependent (non compact) linear operator that governs the dynamics of…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the…
The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and…
Record statistics is the study of how new highs or lows are created and sustained in any dynamical process. The study of the highest or lowest records constitute the study of extreme values. This paper represents an exploration of record…
We investigate some statistical and transport properties of the relativistic standard map. Through the Hamiltonian of a wave packet under an electric potential, we are able to obtain a relativistic version of the standard map, where there…
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself…
In this paper we consider a scalar transport equation with constant coefficients on domains with discrete space and continuous, discrete or general time. We show that on all these underlying domains solutions of the transport equation can…
A network of $N$ elements is studied in terms of a deterministic globally coupled map which can be chaotic. There exists a range of values for the parameters of the map where the number of different macroscopic configurations is very large,…
We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations,…
We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhibit very interesting time-evolving…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…
The distribution of finite time observable averages and transport in low dimensional Hamiltonian systems is studied. Finite time observable average distributions are computed, from which an exponent $\alpha$ characteristic of how the…
We present a new technique in order to quantify the dynamics of spatially extended systems. Using a test on the existence of unstable periodic orbits, we identify intermediate spatial scales, wherein the dynamics is characterized by maximum…
Dynamical scaling in a two-dimensional lattice model of chaotic maps, in contact with a thermal bath, is numerically studied. The model here proposed is equivalent to a conserved Ising model with coupligs which fluctuate over the same time…
Recent investigations in nonlinear sciences show that not only hyperbolic but also mixed dynamical systems may exhibit exponential relaxation in the chaotic regime. The relaxation rates, which lead the decay of probability distributions and…
Robots often have to deal with the challenges of operating in dynamic and sometimes unpredictable environments. Although an occupancy map of the environment is sufficient for navigation of a mobile robot or manipulation tasks with a robotic…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…