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Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in…
It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal…
Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain…
We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular…
It is shown how the macroscopic non-equilibrium dynamics of a class of systems whose microscopic stochastic dynamics involves disordered and frustrated but range-free interactions can be well described by closed deterministic flow…
This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…
In this paper we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify: (i) the discontinuity points of systems described by piecewise dynamical equations…
An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for…
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…
This paper presents a new procedure of generating hash functions which can be evaluated using some mathematical tools. This procedure is based on discrete chaotic iterations. First, it is mathematically proven, that these discrete chaotic…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
This article examines the relationship between classical and quantum propagation of chaos. (In this context, "chaos" refers to the Boltzmann's Ansatz of molecular disorder, not to chaotic dynamics.) Classical propagation of chaos is shown…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
In this short note, we try to provide the reader with a brief pedagogical account of some similarities and differences between stochastic and deterministic processes. A short presentation of some basic notions related to the mathematical…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
We aim to link random fields and marked point processes and therefore introduce a new class of stochastic processes which are defined on a random set in R^d. Unlike for random fields, the mark covariance function of a marked random set is…