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The present paper introduces a new chaos suppression method that is able to stabilize N- dimensional flows by perturbing the state variables in a discrete way when the flow crosses a suitably chosen Poincaré section. Two versions of the method are presented, depending on whether the perturbations are introduced on a proportional or an additive fashion. The perturbations are applied to the corresponding N−1-dimensional Poincaré map, or, in the case of strongly dissipative systems, to a suitable one-dimensional Lorenz map. The method is applied to two different three-variable flows: Rössler spiral chaos model and an isothermal three-variable autocatalator model introduced by Peng et al.

We present an application of the fractal "chaos game representation" method in climatology for characterizing temporal precipitation aggregation patterns. To this aim, we establish an analogy with linguistic analysis considering precipitation as a discrete variable (e.g. rain, no rain). Each weekly, or monthly, symbolic sequence of observed precipitation is then considered a "word" and the climatological time series observed at a particular gauge defines a "language." The distribution of different words within the language characterizes the particular precipitation aggregation scheme. In this paper we show that the chaos game representation method provides a graphical representation (a fractal pattern, or fingerprint) of the distribution of words and also gives a quantitative characterization in terms of parameters such as the box-counting dimension and the entropy. We show that different climates exhibit characteristic patterns with different fractal exponents and entropies. As an illustrative application, the method is used for automatic regionalization of a set of gauges in the Iberian peninsula, showing that these new indices outperform standard averaged statistics (monthly means, etc.).

In this paper, we focus on invariant measures arising from Iterated Function System with Probabilities (IFSP). We show the equivalence between an IFSP and a linear dynamical system driven by a white noise. Then, we use a multifractal analysis to obtain scaling properties of the resulting invariant measures, working within the framework of dynamical systems. Finally, as an application to fractal image generation, we show how this analysis can be used to obtain the most efficient choice for the probabilities to render the attractor of an IFS by applying the probabilistic algorithm known as “chaos game”.

In this paper we present tools for linguistic fractal analysis of symbolic sequences — sequences of formal symbols from a given alphabet. We introduce a method for graphically representing and analyzing symbolic sequences based on fractal Iterated Function Systems (IFSs). This method gives a visual description (a pattern) of the structure of the subsequences within the original sequence, and permits quantitative characterization of the resulting patterns. We present a number of examples and also demonstrate the use of J/Link for importing sequences and speeding up the computations.

The CrossGrid project is one of the ongoing research projects involving GRID technology. One of the main tasks in the Meteorological applications package is the implementation of data mining systems for the analysis of operational and reanalysis databases of atmospheric circulation patterns. Previous parallel data mining algorithms reported in the literature focus on parallel computers with predetermined resources (processing units) and high-performance communications. The main goal in this project is designing adaptive schemes for distributing data and computational load according to the changing resources available for each GRID job submitted. In this paper, some preliminary work regarding two different data mining algorithms (self organizing maps and smoothing filters) is presented. These techniques can be used in combination with databases of observations to provide downscaled local forecasts from operative model outputs. This is a more general and practical framework to look at data mining techniques from the meteorological point of view.