Related papers: Non-statistical behavior via Statistical instabili…
The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…
Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov's theorem, we further investigate the analogous characteristic properties in terms of the sample mean…
Shape-dependent thermodynamics and non-local hydrodynamics are argued to occur in dissipative steady states of driven diffusive systems. These predictions are confirmed by numerical simulations. Unlike power-law correlations, these…
We construct a stochastic dynamical systems theory in which sustainability is a structural boundary property of a fully coupled Earth--Human--Production system. Each subsystem is modelled as a vector-valued process governed by stochastic…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…
While routinely used in other areas of dynamics, image sets are ill-defined objects in general non-invertible measurable dynamics. We propose a way of consistently working with image sets of null-preserving (and hence, in particular, of…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
In this paper we consider an analog of the regions of instability for twist maps in the context of area preserving diffeomorphisms which are not twist maps. Several properties analogous to those of classical regions of instability are…
We study a class of asymptotically entropy-expansive $C^1$ diffeomorphisms with dominated splitting on a compact manifold $M$, that satisfy the specification property. This class includes, in particular, transitive Anosov diffeomorphisms…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
For a twist map $f$ of the annulus preserving the Lebesgue measure, we give sufficient conditions to assure the existence of a set of positive measure of points with non-zero asymptotic torsion. In particular, we deduce that every bounded…
Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the…
We establish the conditioned stochastic stability of equilibrium states for H\"older potentials on uniformly hyperbolic sets. While standard stochastic stability characterises measures on attractors, we analyse the statistics of transient…
The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations.…
Stochastic resetting generates nonequilibrium steady states by interspersing unitary quantum dynamics with resets at random times. When the state to which the system is reset is chosen conditionally on the outcome of a global and spatially…
The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on…