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Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…

In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial…

We introduce a statistical method to detect nonlinearity and nonstationarity in time series, that works even for short sequences and in presence of noise. The method has a discrimination power similar to that of the most advanced estimators…

The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data. As with all system identification methods, noisy measurements…

Nonlinear dynamical systems possessing an invariant subspace can display interesting dynamical behavior, such as on-off intermittency and bubbling. This letter shows that a class of such systems have amazing features of (1) supersensitivity…

Modern data workflows are inherently adaptive, repeatedly querying the same dataset to refine and validate sequential decisions, but such adaptivity can lead to overfitting and invalid statistical inference. Adaptive Data Analysis (ADA)…

This paper is concerned with Devaney chaos in non-autonomous discrete systems. It is shown that in its definition, the two former conditions, i.e., transitivity and density of periodic points, in a set imply the last one, i.e., sensitivity,…

Previous preliminary results on the application of knowledge networks to noise reduction in stationary harmonic and weakly chaotic signals are extended to more general cases. The formalism gives a novel algorithm from which statistical…

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…

Algorithmic differentiation (AD) has become increasingly capable and straightforward to use. However, AD is inefficient when applied directly to solvers, a feature of most engineering analyses. We can leverage implicit differentiation to…

The target of many astronomical studies is the recovery of tiny astrophysical signals living in a sea of uninteresting (but usually dominant) noise. In many contexts (i.e., stellar time-series, or high-contrast imaging, or stellar…

Anomaly detection (AD) is a crucial machine learning task that aims to learn patterns from a set of normal training samples to identify abnormal samples in test data. Most existing AD studies assume that the training and test data are drawn…

This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…

Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…

We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system leave prescribed regions of the state…

We develop the no-propagate algorithm for sampling the linear response of random dynamical systems, which are non-uniform hyperbolic deterministic systems perturbed by noise with smooth density. We first derive a Monte-Carlo type formula…

The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as…

We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…

Noise-based logic is a practically deterministic logic scheme inspired by the randomness of neural spikes and uses a system of uncorrelated stochastic processes and their superposition to represent the logic state. We briefly discuss…

Collective temporal organization in complex systems is commonly attributed to synchronization, resonance, or proximity to dynamical instabilities. Here we identify a distinct mechanism by which coherent, synchronization-like behavior can…