INTERNATIONALJOURNAL
of
CHAOS THEORY  and  APPLICATIONS
Volume 1, Issue # 1, 1996


Editorial
Application Potential of Chaos Theory
   H.N. Teodorescu

Abstract not available

Invited paper
Chaos and Fuzziness? Present and Future
   G. Cocquyt
   Ghent, Belgium

Abstract not available

Regular paper
CANONICAL STATE MODELS FOR HIGHER-ORDER CHAOS SIMULATION IN AUTONOMOUS PIECEWISE-LINEAR DYNAMICAL SYSTEMS
   Jiøí  POSPÍŠIL and   Jaromír  BRZOBOHATÝ
   Technical University of Brno, Department of Radioelectronics, Brno, Czech Republic

Abstract
Two simple state models of the general n-dimensional autonomous piecewise-linear (PWL) dynamical system are proposed. Unlike the known higher order systems usually represented by a chain of coupled Chua's circuits, they are canonical not only with respect to the behaviour (i.e. capable of realizing all possible behaviour of the associated vector field), and with respect to the number of circuit elements (i.e. containing the minimum number of elements necessary), but also with respect to the relation between their parameters and the corresponding eigenvalues. Then the state equations contain minimum nonzero coefficients directly determined by the equivalent eigenvalue parameters associated with the two regions of  PWL vector field. The corresponding integrator-based circuit models and their relation with the known two canonical forms of linear nonautonomous systems are introduced. Finally, the generalized linear topological conjugacy between the third order canonical state models is derived.

Keywords: higer-order chaos, picewise-linear system, canonical state model, topological conguancy.

Regular paper


Analysis and Synthesis of Intelligent Networks for the Identification of Non-Linear Systems:
The Control of the Plasma Shape in Fusion Reactors
   Francesco Carlo Morabito
   University of Reggio Calabria, Faculty of Engineering, Reggio Calabria, Italy

Abstract
Based on the Artificial Neural Network theory, the new notion of composite hidden layer is here proposed as an alternative to the use of just sigmoidal neurons. The introduction of local activation functions, easily related to clustering concept and fuzzy logic approach, allows for a more general and flexible learning fitting. The introduction of other kinds of approximators, like wavelets, is also shown to improve the regression capabilities of the network model without altering the logic of backpropagation. The paper aims to  illustrate the capabilities of the proposed approach for solving a relevant problem in nuclear fusion machines. Some results are presented concerning experimental data taken during a plasma discharge on a real operating tokamak machine. The novel network yields the possibility of automatically implementing a linear mapping, any a priori information available about the problem under study and of approximating data with discontinuities and spikes.

Keywords: Neural Networks, Fuzzy Systems, Hybrid Systems, Inverse Problems, Wavelets, Systems Identification, Non Linear Control

Regular paper
CHUA’S DIODE AND IT’S GENERALIZATION
   Piotr Swiszcz, Janusz Walczak
   Silesian Technical University, Institute of  Theoretical and Industrial Electrotechnics, Gliwice, Poland

Abstract
The one-port called Chua’s diode is a model element which is used for scientific  research  concerning effects in nonlinear systems. A generalisation of Chua’s circuit described by polynomial nonlinearity has been proposed in this article. This system has been realised using analog multipliers and operational amplifiers. Some basic properties of generalised Chua’s circuit have been reported. The simulating research of the elements has been done using PSPICE. A  generalisation of Chua’s circuit is proposed.

 Keywords: nonlinear systems, chaos, Chua's diode

Technical  paper
Software Tools for Analyzing Oscillatory Dynamics in Neural Networks
   Radu Dogaru, Andrei T. Murgan
   Technical University of Bucharest, Applied Electronics Department, Bucharest, Romania

Abstract
A software package for studying discrete time Neural Networks is presented as an efficient analysis tool for studying oscillatory dynamics. A fully-interconnected model for the neural network allows one to study any kind of topology with any dimension (number of neurons) with many kinds of nonlinear activation functions. In this paper synchronous Hopfield networks are investigated by using different strategies for searching in the parameter (weight) space. The first strategy, called two-dimensional analysis, is based on choosing two arbitrary weight parameters that can be varied into a specified domain . For each pair of weights a global descriptor of the network dynamics is computed and then displayed as one pixel of an image. Based on an information theory approach, an entropy associated with a given structure of the network is defined as a global descriptor of the system dynamics. The other strategy assumes  only one weight parameter to be variable and thus it is possible to obtain more information by displaying bifurcation and global descriptor diagrams. Using these software tools, conclusions were derived on the relationship between the gain (hardness) of the activation function and the bifurcation regime. Other results were obtained by introducing a new kind of nonlinearity inspired by the fuzzy membership functions. Using this nonlinearity, robust chaotic regime is achieved even in small neural networks.

Technical  paper
Smoothing Influence on the Answers of a Simple Grassy Ecosystem to Chaos Detection Tests
   D. Creanga, J. Sprott, I. Creanga, I. Bara

Abstract not available

Bulletin Section

No abstracts available

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