Distributional chaos in multifractal analysis, recurrence and transitivity

Distributional uncertainty analysis using power series and polynomial chaos expansions

This paper provides an overview of computationally efficient approaches for quantifying the influence of parameter uncertainties on the states and outputs of nonlinear dynamical systems with finite-time control trajectories, focusing primarily on computing probability distributions. The advantages and disadvantages of various uncertainty analysis approaches, which use approximate representation...

Scale-Free Networks Out of Multifractal Chaos

the stady and analysis of rice agroclimatology in lenjan

the west of esfahan province, iran, is one of the most important agricultural areas throughout the country due to the climate variability and life-giving water of zayanderood river. rice is one of the major and economic crops in this area. the most important climatic elements in agricultural activities which should be considered include temperature, relative humidity, precipitation and wind. so...

Recurrence of Order in Chaos

The standard map x′ = x+y′, y′ = y+(K/2π)sin(2πx), where both x and y are given modulo 1, becomes mostly chaotic for K ≥ 8, but important islands of stability appear in a recurrent way for values of K near K = 2nπ (groups of islands I and II), and K = (2n+1)π (group III), where n ≥ 1. The maximum areas of the islands and the intervals ∆K, where the islands appear, follow power laws. The changes...

RECURRENCE RELATIONS , FRACTALS , AND CHAOS 1 Recurrence Relations , Fractals , and Chaos : Implications for Analyzing Gene Structure

The " chaos game " is a well-known algorithm by which one may construct a pictorial representation of an iterative process. The resulting sets are known as fractals and can be mathematically characterized by measures of dimension as well as by their associated recurrence relations. Using the chaos game algorithm, is it possible to derive meaningful structure out of our own genetic encoding, and...