Skip to main content
SpringerLink
Log in
Book cover

Data-Centric Business and Applications pp 181–205Cite as

Research of Dynamic Processes in the Deterministic Chaos Oscillator Based on the Colpitts Scheme and Optimization of Its Self-oscillatory System Parameters

  • Chapter
  • First Online:

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 48))

Abstract

The results of researching the modern methods and devices of deterministic chaos signal generation, which are constructed on the Colpitts scheme, for the infocommunication systems are given. The main variants for circuitry solutions of the Colpitts chaotic oscillators and their mathematical models are investigated. It is proposed to use voltage-controlled transistor capacitance equivalents on the basis of bipolar transistor structures with negative impedance as capacitive elements of oscillating systems of the Colpitts scheme-based deterministic chaos oscillators. The elements of the theory of the Colpitts scheme-based deterministic chaos oscillators with single-transistor and multi-transistor active elements are presented. The chaotic dynamics of generated electric oscillations and their statistical and informational properties are investigated. Parameters of oscillating systems of the single-transistor and two-transistor Colpitts oscillators for the Kolmogorov-Sinai maximum were optimized. It is established that the maximum Kolmogorov-Sinai entropy is H = 0.1292 for the single-transistor Colpitts oscillator and H = 0.1642 for the two-transistor one with the fractal Hausdorff dimension of dF = 2.1123 and dF = 2.6293 respectively.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Skulysh M (2017) The method of resources involvement scheduling based on the long-term statistics ensuring quality and performance parameters. In: Proceedings of the 2017 international conference on information and telecommunication technologies and radio electronics, Odessa, Ukraine, 11–15 Sept 2017. https://doi.org/10.1109/ukrmico.2017.8095430

  2. Globa L, Skulysh M, Reverchuk A (2014) Control strategy of the input stream on the online charging system in peak load moments. In: Proceedings of the 24th international crimean conference microwave and telecommunication technology, Sevastopol, Ukraine, 7–13 Sept 2014. https://doi.org/10.1109/crmico.2014.6959409

  3. Skulysh M, Romanov O (2018) The structure of a mobile provider network with network functions virtualization. In: Proceedings of the 14th international conference on advanced trends in radioelecrtronics, telecommunications and computer engineering, Lviv-Slavske, Ukraine, 20–24 Feb 2018. https://doi.org/10.1109/tcset.2018.8336370

  4. Globa L, Skulysh M, Zastavenko A (2015) The method of resources allocation for processing requests in online charging system. In: The experience of designing and application of CAD systems in microelectronics, Lviv, Ukraine, 24–27 Feb 2015. https://doi.org/10.1109/cadsm.2015.7230838

  5. Pidchenko S, Taranchuk A (2016) Principles of quartz multifrequency oscillatory systems with digital compensation of temperature and vibrational instability frequency. In: Proceedings of the international conference radio electronics and infocommunications, Kiev, Ukraine, 11–16 Sept 2016. https://doi.org/10.1109/ukrmico.2016.7739620

  6. Pidchenko SK (2013) Dual-frequency temperature-compensated quartz crystal oscillator. In: Proceedings of the 23rd international crimean conference microwave and telecommunication technology, Sevastopol, Ukraine, 8–14 Sept 2013, pp 669–670

    Google Scholar 

  7. Pidchenko S, Taranchuk A (2017) Synthesis of quartz measuring transducers with low Q—factor sensor element. In: Conference proceedings of 2017 IEEE 37th international conference on electronics and nanotechnology, Kyiv, Ukraine, 18–20 April 2017. https://doi.org/10.1109/elnano.2017.7939801

  8. Kychak V et al (2010) Integrated microwave modulator based on induction of dynamic. In: Proceedings of the 2010 international conference on modern problems of radio engineering, telecommunications and computer science, Lviv-Slavske, Ukraine, 23–27 Feb 2010, p 72

    Google Scholar 

  9. Kennedy MP, Rovatti R, Setti G (2000) Chaotic electronics in telecommunications. CRC Press, Inc., Boca Raton, FL, USA

    Google Scholar 

  10. Stavroulakis P (2005) Chaos applications in telecommunications. CRC Press, Taylor and Francis, London

    Book  Google Scholar 

  11. Jovic B (2011) Synchronization techniques for chaotic communication systems. Springer International Publishing, Switzerland

    Book  Google Scholar 

  12. Lau FCM, Tse CK (2003) Chaos-based digital communication systems: operating principles, analysis methods, and performance evaluation. Springer Science and Business Media

    Google Scholar 

  13. Dmitriev AS, Kyarginsky BYe, Panas AI, Starkov SO (2003) Experiments on direct chaotic communications in microwave band. Int J Bifurc Chaos 13(6):1495–1507. https://doi.org/10.1142/s0218127403007345

  14. Dmitriev AS et al (2003) Basic principles of direct Chaotic communications. Nonlinear Phenom Complex Syst 6(1):488–501. https://doi.org/10.1007/978-94-010-0217-2_3

    Article  Google Scholar 

  15. Dmitriev AS, Panas AI, Zakharchenko KV (2003) Principles of direct chaotic communications. In: 2003 IEEE international workshop on workload characterization, vol. 2. Saint Petersburg, Russia, 20–22 Aug 2003, pp 475–483. https://doi.org/10.1109/phycon.2003.1236868

  16. Vovchuk D, Haliuk S, Politanskii L (2014) Experimental research of the process of masking of digital information signals using chaotic oscillation. East Eur Sci J 3:245–253. https://doi.org/10.12851/EESJ201406C06ART09

    Article  Google Scholar 

  17. Efremova EV (2018) Generation of dynamic chaos in a range of 10–30 GHz. J Commun Technol Electron 63(4):367–373. https://doi.org/10.1134/S1064226918040046

    Article  Google Scholar 

  18. Anishchenko VS, Vadivasova TE, Strelkova GI (2014) Deterministic nonlinear systems. Springer International Publishing, Switzerland, A Short Course

    Book  Google Scholar 

  19. IEEE Standard for Information Technology (2007) Telecommunications and in-formation exchange between systems. Local and metropolitan area networks. Specific requirements. Part 15.4: Wireless medium access control (MAC) and Physical layer (PHY) Specifications for low-rate wireless personal area networks (WPANs). Amendment 1: add alternate PHYs

    Google Scholar 

  20. Revision of part 15 of the commission’s rules regarding ultra-wideband transmission systems, first report and order. Federal communications commission (FCC), ET Docket 98–153, FCC 02–48; Adopted: 14 Feb 2002. Released: 22 April 2002

    Google Scholar 

  21. Report from the commission to the european parliament and the council on the implementation of the radio spectrum policy programme, Brussels, 22 April 2014

    Google Scholar 

  22. Aissi C, Kazakos D (2006) A review of chaotic circuits, simulation and implementation. In: Proceedings of the 10th WSEAS international conference on CIRCUITS, Vouliagmeni, Athens, Greece, 10–12 July 2006, pp 125–131

    Google Scholar 

  23. Qiao S, Jiang T, Ran L et al (2007) Ultra-wide band noise-signal radar utilizing microwave chaotic signals and chaos synchronization. In: Progress in electromagnetics research symposium, Prague, Czech Republic, 27–30 Aug 2007, pp 503–506

    Google Scholar 

  24. Tsakiridis O, Syvridis D, Zervas E, Stonham J (2004) Chaotic operation of a Colpitts oscillator in the presence of parasitic capacitances. WSEAS Trans on Electron 1:416–421

    Google Scholar 

  25. Sarkar S, Sarkar S, Sarkar BC (2014) Dynamics of driven Colpitts oscillator in presence of co-channel tone interference: an experimental study. Int J Electron Appl Res 1:1–14

    Google Scholar 

  26. Buscarino A, Fortuna L, Frasca M et al (2010) Chaos control in inductor-based Chaotic oscillators. In: Proceedings of the 19th international symposium on mathematical theory of networks and systems, Budapest, Hungary, 5–9 July 2010, pp 2207–2210

    Google Scholar 

  27. Bonetti RC et al (2014) Super persistent transient in a master–slave configuration with Colpitts oscillators. J Phys A: Math Theor 47(40):405101, pp 1–12. https://doi.org/10.1088/1751-8113/47/40/405101

  28. Kengne J, Chedjou JC, Kenne G et al (2012) Dynamical properties and chaos synchronization of improved Colpitts oscillators. Commun Nonlinear Sci Numer Simul 17(7):2914–2923

    Article  MathSciNet  Google Scholar 

  29. Prodyot KR, Arijit B (2003) A high frequency chaotic signal generator: a demonstration experiment. Am J Phys 71(1):34–37

    Article  Google Scholar 

  30. Kennedy MP (1994) Chaos in the Colpitts oscillator. IEEE transactions on circuits and systems—I: fundamental theory and applications 11:771–774

    Google Scholar 

  31. Cenys A, Tamasevicius A, Baziliauskas A et al (2003) Hyperchaos in coupled Colpitts oscillators. J Chaos, Solitons Fractals 17:349–353

    Article  Google Scholar 

  32. Li GH, Zhou SP, Yang K (2007) Controlling chaos in Colpitts oscillator. Chaos, Solitons Fractals 33:582–587

    Article  Google Scholar 

  33. Semenov A (2016) Reviewing the mathematical models and electrical circuits of deterministic chaos transistor oscillators. In: Proceedings of the international siberian conference on control and communications, Moscow, Russia, 12–14 May 2016. https://doi.org/10.1109/sibcon.2016.7491758

  34. Osadchuk A et al (2008) Mathematical model of transistor equivalent of electrical controlled capacity. In: Proceedings of the international conference modern problems of radio engineering, telecommunication and computer science, Lviv-Slavske, Ukraine, 19–23 Feb 2008, pp 35–36

    Google Scholar 

  35. Semenov A (2016) The Van der Pol’s mathematical model of the voltage-controlled oscillator based on a transistor structure with negative resistance. In: Proceedings of the XIII international conference modern problems of radio engineering, telecommunications, and computer science, Lviv-Slavsko, Ukraine, 23–26 Feb 2016, pp 100–104. https://doi.org/10.1109/tcset.2016.7451982

  36. Semenov A, Osadchuk O, Semenova O et al (2018) Signal statistic and informational parameters of deterministic chaos transistor oscillators for infocommunication systems. In: Proceedings of the 4th international scientific-practical conference problems of infocommunications science and technology, Kharkiv, Ukraine, 9–12 Oct 2018, pp 730–734. https://doi.org/10.1109/infocommst.2018.8632046

  37. Kuznetsov SP (2018) Simple electronic chaos generators and their circuit simulation. Izvestiya VUZ, Appl Nonlinear Dyn 26(3):35–61. https://doi.org/10.18500/0869-6632-2018-26-3-35-61

  38. Garrido PL (1997) Kolmogorov-Sinai entropy, Lyapunov exponents, and mean free time in billiard systems. J Stat Phys 88(3/4):807–824

    Article  MathSciNet  Google Scholar 

  39. Loskutov A (2010) Fascination of chaos. Phys Usp 53(12):1257–1280. https://doi.org/10.3367/UFNr.0180.201012c.1305

    Article  MathSciNet  Google Scholar 

  40. Awrejcewicz J, Krysko AV, Erofeev NP et al (2018) Quantifying chaos by various computational methods. Part 1: simple systems. Entropy 20:175. https://doi.org/10.3390/e20030175

    Article  Google Scholar 

  41. Radivilova T, Kirichenko L, Yeremenko O (2017) Calculation of routing value in MPLS network according to traffic fractal properties. In: Proceedings of the 2nd international conference on advanced information and communication technologies, Lviv, Ukraine, 4–7 July 2017, pp 250–253. https://doi.org/10.1109/aiact.2017.8020112

  42. DEREK—research of dynamic systems. http://derek-ode.sytto.com. Accessed 18 Feb 2019

  43. Bennetin G et al (1980) Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: theory. Meccanica 15(1):9–20. https://doi.org/10.1007/BF02128236

  44. Bennetin G et al (1980) Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 2: numerical application. Meccanica 15(1):21–30. https://doi.org/10.1007/BF02128237

  45. Wegener C, Kennedy MP (1995) RF Chaotic Colpitts oscillator. In: Proceedings of the 3rd international workshop on nonlinear dynamics of electronic systems, Dublin, Ireland, pp 255–258

    Google Scholar 

  46. Mykolaitis G, Tamaševičius A, Bumelienė S et al (2001) HF and VHF chaos oscillators. Electron Electr Eng 32:12–17

    Google Scholar 

  47. Tamaševičius A, Mykolaitis G, Bumelienė S et al (2001) Two-Stage Chaotic Colpitts Oscil Electron Lett 37(9):549–551. https://doi.org/10.1049/el:20010398

    Article  Google Scholar 

  48. Bumelien S, Tamaševicius A, Mykolaitis G et al (2004) Hardware prototype of the two-stage Chaotic Colpitts oscillator for the UHF range. In: Proceedings of the 12th nonlinear dynamics of electronic systems, pp 99–102

    Google Scholar 

  49. Shi ZG, Ran LX (2006) Microwave chaotic Colpitts oscillator: design, implementation and applications. J Electromagn Waves Appl 20(10):1335–1349. https://doi.org/10.1163/156939306779276802

    Article  Google Scholar 

  50. Mykolaitis G, Tamaševičius A, Bumelienė S et al (2004) Two-stage chaotic Colpitts oscillator for the UHF range. Elektronika Ir Elektrotechnika 53:13–15

    Google Scholar 

  51. Lindberg E, Murali K, Tamasevicius A (2008) The Colpitts oscillator family. In: Proceedings of the international symposium: topical problems of nonlinear wave physics, Nizhny Novgorod, NWP-1: Nonlinear Dynamics of Electronic Systems, NDES’2008, 20–26 July 2008, pp 47–48

    Google Scholar 

  52. Semenov A et al (2018) Mathematical modeling of the two-stage Chaotic Colpitis oscillator. In: Proceedings of the 14th international conference on advanced trends in radioelectronics, telecommunications and computer engineering, Lviv-Slavske, Ukraine, 20–24 Feb 2018, pp 835–839. https://doi.org/10.1109/tcset.2018.8336327

  53. Zhang Z et al (2018) Design and nonlinear dynamical performance analysis of novel improved two-stage Colpitts wideband Chaotic oscillator. In: Proceedings of the 2018 IEEE 3rd international conference on image, vision and computing, Chongqing, China, 27–29 June 2018, pp 919–926. https://doi.org/10.1109/icivc.2018.8492812

  54. Chen WL, Zheng LH, Song XX (2016) Design of two-stage chaotic Colpitts oscillator. In: Proceedings of the 2016 IEEE international conference on microwave and millimeter wave technology, Beijing, China, 5–8 June 2016, pp 1029–1031. https://doi.org/10.1109/icmmt.2016.7762523

  55. Semenov A (2016) Mathematical simulation of the chaotic oscillator based on a field-effect transistor structure with negative resistance. In: 2016 IEEE 36th international conference on electronics and nanotechnology (ELNANO), Kyiv, Ukraine, 19–21 April 2016, pp 52–56. https://doi.org/10.1109/elnano.2016.7493008

  56. Osadchuk VS et al (2010) Experimental research and modeling of the microwave oscillator based on the static inductance transistor structure with negative resistance. In: Proceedings of the 20th international crimean conference microwave and telecommunication technology (CriMiCo), Sevastopol, Ukraine, 13–17 Sept 2010, pp 187–188. https://doi.org/10.1109/crmico.2010.5632543

  57. Kirichenko L, Radivilova T (2017) Analyzes of the distributed system load with multifractal input data flows. In: Proceedings of the 14th international conference the experience of designing and application of CAD systems in microelectronics, Lviv, Ukraine, 21–25 Feb 2017, pp 260–264. https://doi.org/10.1109/cadsm.2017.7916130

  58. Radivilova T, Kirichenko L, Ivanisenko Igor (2016) Calculation of distributed system imbalance in condition of multifractal load. In: Proceedings of the third international scientific-practical conference problems of infocommunications science and technology, Kharkiv, Ukraine, 4–6 Oct 2016, pp 156–158. https://doi.org/10.1109/infocommst.2016.7905366

  59. Ivanisenko I, Kirichenko L, Radivilova T (2016) Investigation of multifractal properties of additive data stream. In: Proceedings of the IEEE first international conference on data stream mining and processing, Lviv, Ukraine, 23–27 Aug 2016, pp 305–308. https://doi.org/10.1109/dsmp.2016.7583564

  60. Ivanisenko I, Radivilova T (2015) The multifractal load balancing method. In: Proceedings of the second international scientific-practical conference problems of infocommunications science and technology, Kharkiv, Ukraine, 13–15 Oct 2015, pp 123–123. https://doi.org/10.1109/infocommst.2015.7357289

Download references

Author information

Authors and Affiliations

  1. Vinnytsia National Technical University, Vinnytsia, Ukraine

    Andriy Semenov, Oleksandr Osadchuk, Olena Semenova, Serhii Baraban, Oleksandr Voznyak & Kostyantyn Koval

  2. National University of Water and Environmental Engineering, Rivne, Ukraine

    Andrii Rudyk

Authors
  1. Andriy Semenov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oleksandr Osadchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Olena Semenova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Serhii Baraban
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Oleksandr Voznyak
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Andrii Rudyk
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Kostyantyn Koval
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andriy Semenov .

Editor information

Editors and Affiliations

  1. V.V. Popovskyy department of Infocommunication Engineering, Faculty of Infocommunication, Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

    Tamara Radivilova

  2. V.V. Popovskyy department of Infocommunication Engineering, Faculty of Infocommunication, Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

    Dmytro Ageyev

  3. Department of e-Business, Faculty of Business, Economics and Statistics, University of Vienna, Vienna, Austria

    Natalia Kryvinska

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Semenov, A. et al. (2021). Research of Dynamic Processes in the Deterministic Chaos Oscillator Based on the Colpitts Scheme and Optimization of Its Self-oscillatory System Parameters. In: Radivilova, T., Ageyev, D., Kryvinska, N. (eds) Data-Centric Business and Applications. Lecture Notes on Data Engineering and Communications Technologies, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-030-43070-2_10

Download citation

Publish with us

Policies and ethics

Search

Navigation