Related papers: Dynamical entropy for systems with stochastic pert…
The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase…
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
We explore the chaotic dynamics and complexity of a neuro-system with respect to variable synaptic weights in both noise free and noisy conditions. The chaotic dynamics of the system is investigated by bifurcation analysis and 0-1 test. A…
We study the convergence properties of the conditional (Kullback-Leibler) entropy in stochastic systems. We have proved very general results showing that asymptotic stability is a necessary and sufficient condition for the monotone…
The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given…
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…
We consider the long-time behavior of systems close to a system with a smooth first integral. Under certain assumptions, the limiting behavior, to some extent, turns out to be universal: it is determined by the first integral, the…
We consider the description of quantum noise within the framework of the standard Copenhagen interpretation of quantum mechanics applied to a composite system environment setting. Averaging over the environmental degrees of freedom leads to…
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,…
We investigate quantum systems perturbed by noise in the form of repeated interactions between the system and the environment. As the number of interactions (aka time steps) tends to infinity, we show, following the works by Pellegrini,…
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…
A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. However, one would not only like to infer kinetic parameters but also study their variability…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter…
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…
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…
We consider a finite horizon linear discrete time varying system whose input is a random noise with an imprecisely known probability law. The statistical uncertainty is described by a nonnegative parameter a which constrains the anisotropy…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
We study finite state random dynamical systems (RDS) and their induced Markov chains (MC) as stochastic models for complex dynamics. The linear representation of deterministic maps in RDS are matrix-valued random variables whose…
Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…