INTERNATIONAL  JOURNAL
of
CHAOS THEORY  and  APPLICATIONS
Vol. 4, Issue # 1, 1999


Regular paper
Cantor Sets Ga and L and Their Fractal Dimension
   Petre Bazavan
   University of Craiova, Craiova, Romania

We present three algorithms to build Cantor sets and to determine their fractal dimension.
They are inspired by proofs of certain properties of these sets.

1991 Mathematics Subject Classification: 58F03, 58F08, 58F12, 11K55.
Keywords: Cantor sets, iterated function system, logistic map, generalized box-counting dimension,
algorithms.

Regular paper
A Robust Indirect Adaptive Control for a Class of MIMO Non-Linear Systems
  I. Boumhidi & L. Radouane
  Faculte des Sciences, University of Fes, Maroc

This paper presents a solution to adaptive control of discrete-time linear multi-input multi-output (MIMO)
systems having a polynomial input non-linearity with general time delay structure. The parameter estimation
is the recursive least-squares algorithm with normalisation. The approach is based on using the Chebyshev
orthogonal polynomials for predicting the non-linearity effect, cross-coupling terms and the unmodeled
dynamics. The control law is independently for each subsystems by considering the MIMO system as
composed of MISO (multi-input single-output) subsystems. The system under consideration may be
nonminimum phase. Experimental results verify the effectiveness and robustness of the proposed
approach against unmodeled dynamics.

Key-Words: MIMO systems, adaptive control, non-linear systems, cross-coupling,
decoupling, robustness.

Regular paper
Attractor Control in the Changes of Molecular Vibrations of the Human Lysozyme upon Substrate Binding
   Adriana Isvoran, V.V. Morariu*, A. Negreanu-Maior*
   *West University of Timisoara, Timisoara, Romania
   Institute of Isotopic and Molecular Technology, Cluj-Napoca, Romania

 The characteristics of an attractor control of the changes in molecular vibrations of the human lysozyme
when it reacts with tetra-acetyl-chitotetraose (TAC) have been detected. In this analysis the differences
in the temperature factors of the enzyme with and without TAC were used and the same differences in the
flexibility factors. The Poincaré plots show the preferentially occupied domains, the power spectra are
broad and the autocorrelation functions show the damping expected from the control of an attractor.
The Lyapunov coefficients are positive: 0.185±0.036 for the differences in the temperature factors
and 0.112±0.016 for the differences in the flexibility parameters. The saturation of the integral correlation
coefficient with increasing the number of the coordinates in the phase space indicates the existence of an
attractor of the dimension 2.4±0.22 for the differences in the temperature factors. For the differences in
the flexibility factors the attractor has the dimension 2.1±0.29. The agreement between these results
supports the validity of the hypothesis.

Keywords: chemical model, enzyme, biological processes, enzyme catalysis, attractor control,
molecular vibrations

Brief Technical Note -- Patent Presentations
Two non-classic chaos signal generators
   Horia-Nicolai Teodorescu
   Technical University of Iasi, Iasi, Romania and University of South Florida, Tampa FL, USA

Two chaotic signal generators that do not make use of classic nonlinear systems are presented.
The systems have several advantages, recommending them in specific applications.
Patents were applied for both systems.

Keywords: chaos generators; Barkhausen effect; fuzzy chaotic system

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