INTERNATIONAL  JOURNAL
of
CHAOS THEORY  and  APPLICATIONS
Vol. 3, Issue # 1-2, 1998
Regular paper
Recovering noisy chaotic signals by wavelet transform
    Sumitoshi Ogata*, Noriyuki Murakami** and Takahiro Iwayama*
    *Computer Science and Systems Engineering, Kyushu Institute of Technology Iizuka Fukuoka, 820, Japan
    **TOSHIBA Co., Ltd. 1-1-1 Shibaura Minato Tokyo, 105-01, Japan

We show that wavelet transformation is a useful technique as a low pass filter. We apply this technique to noisy time series, namely a Lorenz signal smeared with random noise and blood velocity data obtained by laser speckle method. One decomposes signals into low and high frequency components based on multi resolution capability of the Mallat transformation. Chaotic pattern appears when we reconstruct a time series using the low frequency component at the third or fourth degradation. The analysis on the blood velocity data indicates not only that a quasi-chaotic pattern appears in the third degradation component but also that the noise separated from the original data is near Gaussian white, showing ideal noise separation.

Keywords: wavelet packets, Mallat transformation, noisy time series, low pass filter, attractor, correlation dimension, Lorenz, blood velocity.

Regular paper
Territorial economic systems and artificial interacting agents: models based on neural networks and cellular automata
Domenico Marino
      Messina University, Italy

The main aim of this paper is to design the connection between economic models and new planning tools (neural networks, cellular automata) in a complex economy. Very interesting features of these systems are: self-organization, learning and self-renforcing mechanisms. These properties are discussed under different points of view in the paper.

Regular paper
A fuzzy information space approach to movement nonlinear analysis
    Wladimir Rodriguez, Horia-Nicolai Teodorescu and Abraham Kandel
     Computer Sciences and Engineering Department, College of Engineering
     University of South Florida, Tampa, Fl, USA

A new approach for analyzing the similarity of dynamical systems is presented. This approach is based on a temporal fuzzy set representation of the trajectories of the dynamical system. The similarity between the dynamical systems is determined based on the density measure of the temporal fuzzy set representing the dynamical system. We present an application of the method to nonlinear movement analysis.

Keywords: fuzzy information space, similarity measure, dynamical systems, chaotic systems, fuzzy classification, medical applications, tremor analysis.

Regular paper
The continuous - discrete models for competition of two species
     L.V.Nedorezov, I.N.Nazarov, O.N.Nazarov
     Institute of Medical and Biological Cybernetics, St. Ac. Timakov , 2, 630117 Novosibirsk, RUSSIA

At present paper, we analyze the various mathematical models of dynamics of isolated population and competition between two species. It is assumed that the death rate of individuals in populations is continuous and appearance of individuals of new generations occurs in some fixed time moments. Dynamic modes of the model under various assumptions about dependencies of death rate and fertility of individuals on the states of populations and influence of winter weather conditions on dynamics of populations are studied. In this paper, we also analyze conditions of "derivation" of classic discrete models of population dynamics, in particular, models of Moran, Ricker and Hassell.

Keywords: Mathematical modeling, Population dynamics, Competition between two species.

Regular paper
Collective effects on individual behavior: Three questions in the search for universality
       I.N. Trofimova, A.B. Potapov and W.H. Sulis*
       Keldysh Institute of Applied Mathematics, Moscow, Russia
       *Departments of Psychiatry, Psychology, and Computer Science, McMaster University, Hamilton, Ontario, Canada

The impact of formal characteristics of population dynamics on individual behavior was studied using a random graphical dynamical model. In this model, agents (individuals) attempted to minimize the costs associated with the establishment of cooperative links with neighboring individuals. These costs varied according to the “compatibility” between agents. The links were dynamic, changing with fluctuations in costs. Population size, compatibilities, sociability and contact rate were tunable parameters. A phase transition was observed as a function of sociability with the critical point Sc = P0,6, where P is the population size. Below Sc, the population organized into a large number of connected small clusters. Above Sc, the population organized mostly into a single large cluster. Such behavior appears to be a group effect, independent of individual characteristics.

Keywords: group dynamics, affiliation, compatibility, random graphs, phase transitions.

Brief overview
Prediction of Chaotic Time Series Through Dynamic Artificial Neural Networks
F. Karray

Abstract not available

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