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Research Papers

Chaotic Synchronization in Ultra-Wide-Band Communication and Positioning Systems

[+] Author and Article Information
J. C. Chedjou1

Institute for Smart Systems Technologies, Transportation Informatics Group (TIG), University of Klagenfurt, Universitätsstrasse 65-67, A-9020, Klagenfurt, Austriajean.chedjou@uni-klu.ac.at

K. Kyamakya

Institute for Smart Systems Technologies, Transportation Informatics Group (TIG), University of Klagenfurt, Universitätsstrasse 65-67, A-9020, Klagenfurt, Austriakyandoghere.kyamakya@uni-klu.ac.at

W. Mathis

Institut für Theoretische Electrotechnik und Hochfrequenztechnik arbeitsgruppe Theoretiische Electrotechnik, Universität Hannover, Appelstrasse 8A, 30467 Hannover, Germanymathis@tet.uni-hannover.de

I. Moussa

Doctoral Unit of Electronics and Information Technology (UDETIME), University of Dschang, P.O. Box 67, Dschang, Cameroon, Africa; Department of Physics, Faculty of Science, University of Yaoundé-I, P.O. Box 812, Yaoundé, Cameroon, Africamoussaildoko@yahoo.fr

A. Fomethe

Doctoral Unit of Electronics and Information Technology (UDETIME), University of Dschang, P.O. Box 67, Dschang, Cameroon, Africa; Polytechnic Institute of Engineering, University of Yaoundé-I, P.O. Box 812, Yaoundé, Cameroon, Africasafomethe@yahoo.fr

V. A. Fono

Doctoral Unit of Electronics and Information Technology (UDETIME), University of Dschang, P.O. Box 67, Dschang, Cameroon, Africafonov2@yahoo.fr

1

Corresponding author.

J. Vib. Acoust 130(1), 011012 (Jan 23, 2008) (12 pages) doi:10.1115/1.2827356 History: Received April 24, 2006; Revised June 03, 2007; Published January 23, 2008

This paper investigates synchronization transitions in a system of coupled Rössler type nonidentical self-sustained chaotic oscillators. The interest in Rössler oscillators is due to their chaotic behavior at very high frequencies. Both phase synchronization and lag synchronization are analyzed numerically considering coupling parameters. It is shown that both types of synchronization can be achieved by monitoring the coupling parameters. The advantage of using one parameter to ensure both types of synchronization is found in practice. Another advantage of monitoring only one resistor is found in the accuracy of results. One resistor is used to predict the boundaries of the control resistor for the occurrence of each type of synchronization. An experimental study of the synchronization is carried out in this paper. An appropriate electronic circuit describing the coupled oscillators is designed and realized. Experimental wave forms in the drive and response systems are obtained and their comparison done to confirm the achievement of synchronization. The analog simulation is advantageous to analyze the behavior of the coupled system at very high frequencies at appropriate time scaling and offers the possibility of using our coupled system for ultra-wide-band applications.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Projection of the attractors in the plan (x1(t),x2(t)) and (x1(t),x2(t+τ0)) showing both chaotic (ε2=0.0158 and ε2=0.0178) and regular (ε2=0.028 and ε2=0.030) LSs in terms of the coupling parameter ε2. The values of the lag time τ0 and the system parameters are defined in the text.

Grahic Jump Location
Figure 2

Projection of the attractors in the plan (x1(t),x2(t)) and (x1(t),x2(t+τ0)) showing both chaotic (ε3=0.0143 and ε3=0.020) and regular (ε3=0.017 and ε3=0.028) LSs in terms of the coupling parameter ε3. The values of the lag time τ0 and the system parameters are defined in the text.

Grahic Jump Location
Figure 3

Temporal development of the phase difference between the drive and response systems, respectively, in the states of imperfect PS (ε3=0.075) and PS (ε3=0.350, ε3=0.69352, and ε3=0.980). The values of the system parameters are defined in the text.

Grahic Jump Location
Figure 4

Schematic representation of the complete circuit representing the three coupled oscillators (drive-response-auxiliary)

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Figure 5

Physical implementation of Fig. 4

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Figure 6

Chaotic phase portrait of the auxiliary system obtained numerically (a) and its corresponding experimental phase portrait (b) at the decoupled states of the drive, response, and auxiliary systems. The corresponding parameters are defined in the text.

Grahic Jump Location
Figure 7

Chaotic phase portrait of the drive system obtained numerically (a) and its corresponding experimental phase portrait (b) at the decoupled states of the drive, response, and auxiliary systems. The corresponding parameters are defined in the text.

Grahic Jump Location
Figure 8

Numerical and experimental projections of the attractors in the plan (x1(t),x2(t)) in the case of regular and chaotic synchronizations: P11 and P12:R29=633kΩ(ε2=0.0158), P21 and P22:R29=562kΩ(ε2=0.0178), P31 and P32:R29=357kΩ(ε2=0.028), and P41 and P42:R29=333kΩ(ε2=0.03). Same values of the system parameters in Fig. 7 with R19=833kΩ and R39=500kΩ.

Grahic Jump Location
Figure 9

Numerical and experimental projections of the attractors in the plan (x1(t),x2(t)) in the case of regular and chaotic synchronizations: P11 and P12:R39=699.5kΩ(ε3=0.0143), P21 and P22:R39=588kΩ(ε3=0.017), P31 and P32:R39=500kΩ(ε3=0.020), and P41 and P42:R39=357kΩ(ε3=0.028). Same values of the system parameters in Fig. 7 with R19=833kΩ and R29=568kΩ.

Grahic Jump Location
Figure 10

Pictures of the experimental wave forms in the case of chaotic synchronization: (a) drive and (b) response obtained using the same values in Fig. 7 with R19=833kΩ, R29=562kΩ, and R39=500kΩ

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