Synchronization of Chaotic Oscillators Operating in theUHF Band Using the Adaptive Observer Method

Authors

  • Franklin Djimasra
  • Jean De Dieu Nkapkop
  • Nestor Tsafack
  • Abdelkrim Boukabou
  • Jean Yves Effa

Keywords:

Chaos, synchronization, Hartley oscillator, Colpitts oscillator, UHF band

Abstract

In this work, we consider the synchronization between chaotic oscillators with di?erent orders and operating in the UHF band. Firstly, the normalized state equation of Hartley and Colpitts oscillators are presented as well as their chaotic behavior has been proven in this frequency band. Secondly, the problem of dynamics synchronization is investigated, and a controller based on Lyapunov stability theory is proposed to ensure synchronization between both oscillators. Finally, computer experiments are provided to demonstrate the e?ectiveness and feasibility of the proposed synchronization approach.

Author Biographies

  • Franklin Djimasra

    Department of Fundamental Sciences, University of Moundou, B.P. 206 Moundou, Tchad

  • Jean De Dieu Nkapkop

    Department of Electrical Engineering and Industrial Computing, University Institute of Technology, P.O. Box 8698 Douala, Cameroon

  • Nestor Tsafack

    Research Unit of Laboratory of Condensed Matter, Electronics and Signal Processing(URMACETS)

  • Abdelkrim Boukabou

    Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

  • Jean Yves Effa

    Department of Electronics, University of MSB Jijel, Ouled Aissa, Jijel 18000, Algeria

References

[1] L. M. Pecora and T. L. Carroll. “Synchronization in chaotic systems”. Phys. Rev. Lett. Vol. 64, pp. 821-824, 1990.

[2] Terry J.R and Vanwiggeren G.D. “Chaotic communication using generalized synchronization”. Chaos Solitons Fractals. Vol. 12, pp. 145-152, 2001.

[3] Guo X. W and Shu L. Q. “Chemical chaotic schemes derived from NSG system”. Chaos Solitons Fractals. Vol. 15, pp. 663-671, 2003.

[4] Petrovskii S., Li. B. L. and Malchow H. “Quantification of spatial aspect of chaotic dynamic in biological and chemical systems”. Bull. Math. Boil. Vol. 65, pp. 425-446, 2003.

[5] Kennedy MP. “Chaos in the Colpitts oscillator”. IEEE Trans Circ Syst I, Vol. 41, pp.771–784.

[6] Wegener C, Kennedy MP. “RF chaotic Colpitts oscillator”. In Proc. of an international workshop on nonlinear dynamics of electronic systems NDES, Dublin Ireland, 1995, pp. 255–8.

[7] Mykolaitis G, Tamasevicius A, Bumeliene S. “Experimental demonstration of chaos from the Colpitts oscillator in the VHF and the UHF ranges”. Electron Lett, Vol. 40, pp. 91–2, 2004.

[8] Elwakil AS, Kennedy MP. “Construction of classes of circuit- independent chaotic oscillators using passive-only nonlinear devices”. IEEE Trans. Vol. 48, pp. 289-307, 2001.

[9] Elshabini-Riad Aicha, Stephenson F. W, Bhutta Imran. “Electrical Equivalent Circuit Models and Device Simulators for Semiconductor Devices”. In Dorf Richard C., editor. The Electrical Engineering Handbook. Boca Raton: CRC Press LLC, 2000.

[10] Tamasevicius A, Cenys A, Mykolaitis G, Namajunas A. “Synchronization of chaos and its application to secure communication”. Lithuanian J Phys, Vol.38, pp.33–7, 1998.

[11] Uchida A, Kawano M, Yoshomori S. “Dual Synchronization of chaos in Colpitts electronic oscillators and its applications for communications”. Phy. Rev. Vol. 68:56207:1–056207:11.

[12] Qiao S, Shi ZG, Chen KS, Cui WZ, Ma W, Jiang T, et al. “A new architecture of UWB radar utilizing microwave chaotic signals and chaos synchronization”. Prog Electromagnetics Res PIER, 2007, Vol. 75, pp. 225–37.

[13] Tamasevicius A, Mykolaitis G, Bumeliene S, Cenys A, Lindberg E.. “Synchronization of VHF chaotic Colpitts oscillator, in: Proceedings 17of international workshop on nonlinear dynamics of electronic systems NDES’97”. Delft Netherlands; pp. 223–6, 2001.

[14] Rubezic V, Ostojic R. “Synchonization of chaotic Colpitts oscillator with applications to binary communications”. In Proc. ICECS, 1999, pp. 153–6.

[15] Burykin VA, Panas AI (1997). “Chaotic synchronization of RF generators”. In Proc. NDES 1997, Moscow Russia; pp. 548–53.

[16] Baziliauskas A, Krivickas R, Tamasevicius A. “Coupled chaotic Colpitts oscillator: identical and mismatched cases”. Nonlinear Dynam, Vol. 44, pp. 151–8, 2006.

[17] Fotsin HB, Daafouz J. “Adaptive synchronization of uncertain chaotic Colpitts oscillators based on parameter identification”. Phys Lett A, Vol. 339, pp. 304–15, 2005.

[18] Li GH. “Synchronization and anti-synchronization of Colpitts oscillators using active control”. Chaos Soliton Fract, Vol. 26, pp. 87–93, 2005.

[19] Cenys A, Tamasevicius A, Mykolaitis G. “Hyperchaos and synchronization in mean field coupled chaotic oscillator”. In Proc. NOLTA, 1998, Crans-Montana Switzerland; pp. 519–40.

[20] Li GH. “Chaos and synchronization of Colpitts oscillators”. Microwave Opt Technol Lett, Vol. 39, pp. 446–9, 2003.

[21] Liao TL, Tsai SH. “Adaptive synchronization of chaotic systems and its application to secure communications”. Chaos Soliton Fract, Vol. 11, pp. 1387–96, 2000.

[22] L¨u L, Luan L, Guo ZA (2007). “Synchronization of chaotic systems with different orders”. Chin Phys, Vol. 16, pp. 06–346.

[23] Baars G. “Hartley-oscillatormitnurzweiBauteilen”.Elektor.Vol.29, pp.7-8. 18, 2002.

[24] Attia J. O. “Transistor circuits”. In Attia John Okyere, editor.Electronics and circuits analysis using MATLAB, 1999. Boca Raton: CRC Press LLC.

[25] Sprott J. C. “Chaos and time-series analysis”. New York: Oxford University Press, 2003.

[26] Chua L. O. (1992). “The genesis of Chua’s circuit”. Stuttgart: HirzelVerlag. AEU 46, pp. 250-257.

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Published

2026-01-26

Issue

Vol. 78 No. 1 (2025)

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How to Cite

Franklin Djimasra, Jean De Dieu Nkapkop, Nestor Tsafack, Abdelkrim Boukabou, & Jean Yves Effa. (2026). Synchronization of Chaotic Oscillators Operating in theUHF Band Using the Adaptive Observer Method. International Journal of Sciences: Basic and Applied Research (IJSBAR), 78(1), 510-527. https://www.gssrr.org/JournalOfBasicAndApplied/article/view/17657