Stochastic models of chaotic systems

Stochastic Models of Chaotic Systems

Nonlinear dynamical systems, although strictly deterministic, often exhibit chaotic . behavior which appears to be random. The determination of the probabilistic prop ertics of such systems is, in general, an open problem. Closure approximations for moment expansion methods have been unsatisfactory. More successful has been approximation on the dynamics level by the use of linear stochastic mod...

Stochastic Resonance in Deterministic Chaotic Systems

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 threshold for the onset of chaos, stochastic resonance effects appears. As a result one has an alternation of chaotic and regular, i.e. predictable, evolutions in...

Models of Stochastic Systems

Preservation of Stochastic Orderings of Interdependent Series and Parallel Systems by Componentwise Switching to Exponentiated Models

This paper discusses the preservation of some stochastic orders between two interdependent series and parallel systems when the survival and distribution functions of all components switch to the exponentiated model. For the series systems, the likelihood ratio, hazard rate, usual, aging faster, aging intensity, convex transform, star, superadditive and dispersive orderings, and for the paralle...

Simple Models of Complex Chaotic Systems

Many phenomena in the real world are inherently complex and involve many dynamical variables interacting nonlinearly through feedback loops and exhibiting chaos, self-organization, and pattern formation. It is useful to ask if there are generic features of such systems, and if so, how simple can such systems be and still display these features. This paper describes several such systems that are...