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

 
 


Editorial
Dynamic Sensitivity Analysis
    Horia-Nicolai Teodorescu
Regular paper
The Attractors of Some Contractive Dynamical Processes
   Dana Constantinescu and Maria Predoi
   Faculty of Mathematics and Informatics, University of Craiova, Craiova, Romania

Abstract. In this paper we study the contractive dynamical processes attractors and we obtain, as a particular case, some well-known results about the attractors of contractive dynamical systems. Several applications in the approximation of iterated function systems attractors are derived.

Keywords: dynamical systems, attractors, iterated function systems, chaos, fractals
1991 Mathematics Subject Classification:: 58F13, 54H20

Regular paper
Digital Encryption based on Exact Chaos Synchronization
  Victor Grigoras
  Technical University of Iasi, Iasi, Romania

Abstract. The inverse system approach, applied to digital filter type chaotic circuits, is used to build the encryption and decription algorithms. Conditions for filter coefficients and channel quantization step, in order to achieve perfect synchronization, are proved. In depth simulations are presented.

Keywords: discrete-time chaotic system, chaos synchronization, digital encryption

Regular paper
The Dynamical System Generated by a Variable Step-size Algorithm for Runge-Kutta Methods
  Petre Bazavan
  University of Craiova, Faculty of Mathematics and Informatics,
  A.I. Cuza, 13, 1100, Craiova, Romania, e-mail bazavan@yahoo.com

Abstract. We prove that the variable step-size algorithm for Runge-Kutta methods, proposed in [7], generates a dynamical system whose orbits approximate the orbits of the dynamical system associated with the system of ordinary differential equations (ODEs) to which is applied the algorithm.

Keywords: Runge-Kutta methods, variable step-size, dynamical systems, approximation, orbit convergence.

Regular paper
Analysis of Chaos  in Circuits Based on Wien Oscillators
X. Peillon*, H.N. Teodorescu**, A. Kandel***, D. Mlynek*
* Swiss Federal Institute of Technology, Lausanne
** University of South Florida, USA, and Romanian Academy, Institute for Information Science , Iasi
*** University of South Florida, Tampa, FL, USA
Abstract. This paper presents the behavior of several types of Wien oscillators modified for chaos [1] using real operational amplifiers. Several aspects are investigated, including the influence of parasitic elements, variation of the tolerances of the components, influence of the PSPICE modeling, influence of the computation precision on simulated chaotic behavior. The modeling results are compared with experimental observations.
We show the possibility to synchronize such circuits so as to control the system sensitivity. Experimental measures and PSPICE results are provided for the Wien bridge oscillators.
Investigating the behavior of networks including several chaotic Wien oscillators, we remark that it was very interesting in view to create a new family of chaotic circuits.

Keywords: chaotic Wien oscillators, sensitivity analysis, SPICE modeling, parameter tollerance, temperature sensitivity

Regular paper
Chaotic series forecasting by neurons with fuzzy synapses
   Ioan Mircea Chelaru
   Duke University, Durham, NC, 27708, USA

Abstract. The paper presents a fuzzy neuron with fuzzy synapses and the corresponding training algorithm.The neuron is a generalization of the Yamakawa fuzzy neuron. The predictive power of this neuron is demonstrated on several well-known chaotic time series.

Keywords: fuzzy neuron, fuzzy synases, prediction

Bulletin Section

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