IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v73y2015icp17-28.html
   My bibliography  Save this article

De-synchronization and chaos in two inductively coupled Van der Pol auto-generators

Author

Listed:
  • Beregov, R.Y.
  • Melkikh, A.V.

Abstract

In this article, we consider a system of autonomous inductively coupled Van der Pol generators. For two coupled generators, we establish the presence of metastable chaos, a strange non-chaotic attractor, and several stable limiting cycles. Areas of parametric dependence of different modes of synchronization are obtained.

Suggested Citation

  • Beregov, R.Y. & Melkikh, A.V., 2015. "De-synchronization and chaos in two inductively coupled Van der Pol auto-generators," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 17-28.
    • Handle: RePEc:eee:chsofr:v:73:y:2015:i:c:p:17-28
    DOI: 10.1016/j.chaos.2014.12.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077914002379
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2014.12.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Leung, H.K., 2003. "Synchronization dynamics of coupled van der Pol systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(1), pages 248-255.
    2. Tal Danino & Octavio Mondragón-Palomino & Lev Tsimring & Jeff Hasty, 2010. "A synchronized quorum of genetic clocks," Nature, Nature, vol. 463(7279), pages 326-330, January.
    3. Kimiaeifar, A. & Saidi, A.R. & Bagheri, G.H. & Rahimpour, M. & Domairry, D.G., 2009. "Analytical solution for Van der Pol–Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2660-2666.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Masa Tsuchiya & Vincent Piras & Alessandro Giuliani & Masaru Tomita & Kumar Selvarajoo, 2010. "Collective Dynamics of Specific Gene Ensembles Crucial for Neutrophil Differentiation: The Existence of Genome Vehicles Revealed," PLOS ONE, Public Library of Science, vol. 5(8), pages 1-10, August.
    2. Onelia Gagliano & Camilla Luni & Yan Li & Silvia Angiolillo & Wei Qin & Francesco Panariello & Davide Cacchiarelli & Joseph S. Takahashi & Nicola Elvassore, 2021. "Synchronization between peripheral circadian clock and feeding-fasting cycles in microfluidic device sustains oscillatory pattern of transcriptome," Nature Communications, Nature, vol. 12(1), pages 1-12, December.
    3. Lukas Aufinger & Johann Brenner & Friedrich C. Simmel, 2022. "Complex dynamics in a synchronized cell-free genetic clock," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    4. Singh, Vijai & Chaudhary, Dharmendra Kumar & Mani, Indra & Dhar, Pawan Kumar, 2016. "Recent advances and challenges of the use of cyanobacteria towards the production of biofuels," Renewable and Sustainable Energy Reviews, Elsevier, vol. 60(C), pages 1-10.
    5. Lucas Henrion & Juan Andres Martinez & Vincent Vandenbroucke & Mathéo Delvenne & Samuel Telek & Andrew Zicler & Alexander Grünberger & Frank Delvigne, 2023. "Fitness cost associated with cell phenotypic switching drives population diversification dynamics and controllability," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    6. Navneet Rai & Rajat Anand & Krishna Ramkumar & Varun Sreenivasan & Sugat Dabholkar & K V Venkatesh & Mukund Thattai, 2012. "Prediction by Promoter Logic in Bacterial Quorum Sensing," PLOS Computational Biology, Public Library of Science, vol. 8(1), pages 1-14, January.
    7. Volkov, Evgeny & Hellen, Edward H., 2021. "The effect of characteristic times on collective modes of two quorum sensing coupled identical ring oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    8. Alice Boo & Tyler Toth & Qiguo Yu & Alexander Pfotenhauer & Brandon D. Fields & Scott C. Lenaghan & C. Neal Stewart & Christopher A. Voigt, 2024. "Synthetic microbe-to-plant communication channels," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    9. Youhua Qian & Shuli Wang & Shuping Chen, 2023. "Multi-Frequency Homotopy Analysis Method for Coupled Van der Pol-Duffing System with Time Delay," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
    10. Yu-Yu Cheng & Zhengyi Chen & Xinyun Cao & Tyler D. Ross & Tanya G. Falbel & Briana M. Burton & Ophelia S. Venturelli, 2023. "Programming bacteria for multiplexed DNA detection," Nature Communications, Nature, vol. 14(1), pages 1-11, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:73:y:2015:i:c:p:17-28. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.