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Coupled inductors-based chaotic Colpitts oscillators: Mathematical modeling and synchronization issues

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Abstract

This paper deals with the mathematical modelling and synchronization of a new controlled Colpitts oscillator. The new electronic oscillator is constructed by considering standard/classical Colpitts oscillator with two further elements (coupled inductors and variable resistor). An accurate mathematical model is provided. The dynamics of the new controlled Colpitts oscillator is investigated theoretically and experimentally by examining dissipativity, equilibrium point, stability, bifurcation and Lyapunov exponent. It is found that the oscillator moves from the limit cycle motion to chaos via the usual paths of period-doubling, intermittency and interior crisis routes as the control resistor R L is monitored. The electronic circuit of the oscillator is implemented, and a very good qualitative agreement is obtained between the theoretical and experimental results. Furthermore, the problem of synchronization is investigated, in order to promote chaos-based synchronization designs of this type of oscillators. Firstly, we design a coupling function for unidirectional coupling in identical and mismatched controlled Colpitts oscillators to realize a modified function projective synchronization through the open-plus-closed-loop (OPCL) method. Secondly, two different coupling configurations, namely, coupled collector nodes (C-C) and coupled emitter nodes (E-E) of controlled Colpitts oscillators, are studied. Numerical simulations and experimental results are performed to show the effectiveness and robustness of the proposed control schemes.

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Authors and Affiliations

  1. Laboratory of Electronics and Signal Processing (LETS), Department of Physics, Faculty of Science, University of Dschang, P. O. Box: 67, Dschang, Cameroon

    V. Kamdoum Tamba & H. B. Fotsin

  2. Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P. O. Box: 134, Bandjoun, Cameroon

    V. Kamdoum Tamba & F. Kapche Tagne

  3. Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P. O. Box: 134, Bandjoun, Cameroon

    J. Kengne

  4. Laboratory of Mechanics and Modelling of Physical Systems (L2MPS), Department of Physics, Faculty of Science, University of Dschang, P. O. Box: 67, Dschang, Cameroon

    P. K. Talla

Authors
  1. V. Kamdoum Tamba
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  2. H. B. Fotsin
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  3. J. Kengne
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  4. F. Kapche Tagne
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  5. P. K. Talla
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Correspondence to H. B. Fotsin.

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Kamdoum Tamba, V., Fotsin, H.B., Kengne, J. et al. Coupled inductors-based chaotic Colpitts oscillators: Mathematical modeling and synchronization issues. Eur. Phys. J. Plus 130, 137 (2015). https://doi.org/10.1140/epjp/i2015-15137-x

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  • DOI: https://doi.org/10.1140/epjp/i2015-15137-x

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