Hyperchaos in coupled Colpitts oscillators

Antanas Cenys, Arunas Tamasevicius, Antanas Baziliauskas, Romanas Krivickas, Erik Lindberg

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Abstract

The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R-k. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual chaotic signals, v(t) = (v(1) + v(2))/2. The corresponding differential equations have been derived. The results of both, numerical simulations and hardware experiments are presented. The coupling coefficient k proportional to 1/R-k should be small to avoid mutual synchronisation of the individual oscillators. The spectrum of the Lyapunov exponents (LE) have been calculated versus the coefficient k. For weakly coupled oscillators there are two positive LE indicating hyperchaotic behaviour of the overall system.
Original languageEnglish
JournalChaos, Solitons & Fractals
Volume17
Issue number2-3
Pages (from-to)349-353
ISSN0960-0779
Publication statusPublished - 2003

Cite this

Cenys, A., Tamasevicius, A., Baziliauskas, A., Krivickas, R., & Lindberg, E. (2003). Hyperchaos in coupled Colpitts oscillators. Chaos, Solitons & Fractals, 17(2-3), 349-353.
Cenys, Antanas ; Tamasevicius, Arunas ; Baziliauskas, Antanas ; Krivickas, Romanas ; Lindberg, Erik. / Hyperchaos in coupled Colpitts oscillators. In: Chaos, Solitons & Fractals. 2003 ; Vol. 17, No. 2-3. pp. 349-353.
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Cenys, A, Tamasevicius, A, Baziliauskas, A, Krivickas, R & Lindberg, E 2003, 'Hyperchaos in coupled Colpitts oscillators', Chaos, Solitons & Fractals, vol. 17, no. 2-3, pp. 349-353.

Hyperchaos in coupled Colpitts oscillators. / Cenys, Antanas; Tamasevicius, Arunas; Baziliauskas, Antanas; Krivickas, Romanas; Lindberg, Erik.

In: Chaos, Solitons & Fractals, Vol. 17, No. 2-3, 2003, p. 349-353.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Hyperchaos in coupled Colpitts oscillators

AU - Cenys, Antanas

AU - Tamasevicius, Arunas

AU - Baziliauskas, Antanas

AU - Krivickas, Romanas

AU - Lindberg, Erik

PY - 2003

Y1 - 2003

N2 - The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R-k. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual chaotic signals, v(t) = (v(1) + v(2))/2. The corresponding differential equations have been derived. The results of both, numerical simulations and hardware experiments are presented. The coupling coefficient k proportional to 1/R-k should be small to avoid mutual synchronisation of the individual oscillators. The spectrum of the Lyapunov exponents (LE) have been calculated versus the coefficient k. For weakly coupled oscillators there are two positive LE indicating hyperchaotic behaviour of the overall system.

AB - The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R-k. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual chaotic signals, v(t) = (v(1) + v(2))/2. The corresponding differential equations have been derived. The results of both, numerical simulations and hardware experiments are presented. The coupling coefficient k proportional to 1/R-k should be small to avoid mutual synchronisation of the individual oscillators. The spectrum of the Lyapunov exponents (LE) have been calculated versus the coefficient k. For weakly coupled oscillators there are two positive LE indicating hyperchaotic behaviour of the overall system.

M3 - Journal article

VL - 17

SP - 349

EP - 353

JO - Chaos, Solitons & Fractals

JF - Chaos, Solitons & Fractals

SN - 0960-0779

IS - 2-3

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Cenys A, Tamasevicius A, Baziliauskas A, Krivickas R, Lindberg E. Hyperchaos in coupled Colpitts oscillators. Chaos, Solitons & Fractals. 2003;17(2-3):349-353.