相关论文: Uncovering low dimensional macroscopic chaotic dyn…

We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…

We characterize the macroscopic attractor of infinite populations of noisy maps subjected to global and strong coupling by using an expansion in order parameters. We show that for any noise amplitude there exists a large region of strong…

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…

Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…

We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…

It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…

We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…

We present a data-driven and interpretable approach for reducing the dimensionality of chaotic systems using spectral submanifolds (SSMs). Emanating from fixed points or periodic orbits, these SSMs are low-dimensional inertial manifolds…

Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…

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…

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…

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…

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…

We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…

It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the…

Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of…

We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…

The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…

An investigation of the mesoscopic dynamics of chemical systems whose mass action equation gives rise to a deterministic chaotic attractor is carried out. A reactive lattice-gas model for the three-variable autocatalator is used to provide…