Related papers: Noise-enhanced reconstruction of attractors
We study an extended system that without noise shows a spatially homogeneous state, but when submitted to an adequate multiplicative noise, some "noise-induced patterns" arise. The stochastic resonance between these structures is…
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.
Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from time series data of a scalar observable,…
The method of reconstruction of an attractor from a set of short time series ({\it clusters}) is proposed and discussed. This method is most useful for correlation dimension estimation of experimental data.
Stochastic resetting and noise-enhanced stability are two phenomena which can affect the lifetime and relaxation of nonequilibrium states. They can be considered as measures of controlling the efficiency of the completion process when a…
Stochastic resonance is a non-linear phenomenon, in which the sensitivity of signal detectors can be enhanced by adding random noise to the detector input. Here, we demonstrate that noise can also improve the information flux in recurrent…
This paper proposes a chaos-based analog-to-information conversion system for the acquisition and reconstruction of sparse analog signals. The sparse signal acts as an excitation term of a continuous-time chaotic system and the compressive…
Anatomical studies demonstrate that brain reformats input information to generate reliable responses for performing computations. However, it remains unclear how neural circuits encode complex spatio-temporal patterns. We show that neural…
Stochastic and coherence resonances appear in nonlinear systems subjected to an external source of noise and are characterized by a maximum response at the optimal value of the noise intensity. This paper shows experimentally that it is…
We propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that…
We undertake a preliminary numerical investigation to understand how the addition of white and colored noise to a time series affects the topology and structure of the underlying chaotic attractor. We use the methods and measures of…
In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. This statistics can be evaluated on any reconstructed attractor, thereby allowing a…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the…
We have analyzed the interplay between noise and periodic spatial modulations in bistable systems outside equilibrium and found that noise is able to increase the spatial order of the system, giving rise to periodic patterns which otherwise…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
A method for the quantitative analysis of the degree and parameters of synchronization of the chaotic oscillations in two coupled oscillators is proposed, which makes it possible to reveal a change in the structure of attractors. The…
The phenomenon of Stochastic Resonance (SR) is observed in a completely deterministic setting - with thermal noise being replaced by one-dimensional chaos. The piecewise linear map investigated in the paper shows a transition from…