In this article a symbolic Mathematica package for analysis and control of chaos in discrete and continuous nonlinear systems is presented. We start by presenting the main properties of chaos and describing some commands with which to obtain qualitative and quantitative measures of chaos, such as the bifurcation diagram and the Lyapunov exponents, respectively. Then we analyze the problem of ch...

What is the optimal level of chaos in a computational system? If a system is too chaotic, it cannot reliably store information. If it is too ordered, it cannot transmit information. A variety of computational systems exhibit dynamics at the “edge of chaos”, the transition between the ordered and chaotic regimes. In this work, we examine the evolved neural networks of Polyworld, an artificial li...

The Dramatica Theory was developed by Melanie Anne Phillips and Chris Huntley and was not researched nor based upon any other theories of story design or analysis. Trademarks Dramatica is a registered trademark of Screenplay Systems Incorporated. Dramatica's terminology has its own grammar with structures, designations , and usages which are reflected in the vocabulary listings. The individual ...

This paper examines the most probable route to chaos in high-dimensional dynamical systems function space (time-delay neural networks) endowed with a probability measure in a computational setting . The most probable route to chaos (relative to the measure we impose on the function space) as the dimension is increased is observed to be a sequence of Neimark-Sacker bifurcations into chaos. The a...

BACKGROUND In a previous work (Dafilis et al. in Chaos 23(2):023111, 2013), evidence was presented for four-dimensional chaos in Liley's mesoscopic model of the electroencephalogram. The study was limited to one parameter set of the model equations. FINDINGS In this report we expand that result by presenting evidence for the extension of four-dimensional chaotic behavior to a large area of th...

Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major dr...

Abstract: Consider a mathematical model with a finite number of random parameters. Variance based sensitivity analysis provides a framework to characterize the contribution of the individual parameters to the total variance of the model response. We consider the spectral methods for variance based sensitivity analysis which utilize representations of square integrable random variables in a gene...

Road traffic volumes in intercity roads are generally estimated by probability functions, statistical techniques or meta-heuristic approaches such as artificial neural networks. As the road traffic volumes depend on input variables and mainly road geometrical design, weather conditions, day or night time, weekend or national holidays and so on, these are also estimated by pattern recognition te...

A new methodology for a robust analysis of uncertain nonlinear dynamic systems is presented in this paper. The originality of the method proposed lies in the combination of the centre manifold theory with the polynomial chaos approach. The first one is known to be a powerful tool for model reduction of nonlinear dynamic systems in the neighbourhood of the Hopf bifurcation point while the polyno...