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Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level,…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Uncertainty plays a key role in future prediction. The future is uncertain. That means there might be many possible futures. A future prediction method should cover the whole possibilities to be robust. In autonomous driving, covering…
The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application to Physics problems requires attention…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
While noise is generally associated with uncertainties and often has a negative connotation in engineering, living organisms have evolved to adapt to (and even exploit) such uncertainty to ensure the survival of a species or implement…
We study the evolution of a system of interacting ultracold bosons, which presents nonlinear, chaotic, behaviors in the limit of very large number of particles. Using the spectral entropy as an indicator of chaos and three different…
In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations…
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…
Despite the celebrated success of stochastic control approaches for uncertain systems, such approaches are limited in the ability to handle non-Gaussian uncertainties. This work presents an adaptive robust control for linear uncertain…
The dichotomy between noise-stable and (completely) noise-sensitive stochastic models is of recent interest in probability theory. Of particular interest is the study of lattice models coming from statistical physics. The Fourier transform…
We study stochastic dynamical systems in settings where only partial statistical information about the noise is available, e.g., in the form of a limited number of noise realizations. Such systems are particularly challenging to analyze and…
Dynamical behaviors of a dissipative particle in a periodic potential subject to chaotic noise are reported. We discovered a macroscopic symmetry breaking effect of chaotic noise on a dissipative particle in a multi-stable systems emerging,…
We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former…
Noise-induced failures in the stabilization of an unstable orbit in the one-dimensional logistic map are considered as large fluctuations from a stable state. The properties of the large fluctuations are examined by determination and…
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…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
Simple dynamical systems -- with a small number of degrees of freedom -- can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small…
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature…
Motivated by stochastic models of climate phenomena, the steady-state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady-states provide a constraint on the character of…