IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v51y2013icp36-51.html
   My bibliography  Save this article

Arbitrary waveform generator biologically inspired

Author

Listed:
  • Vázquez-Medina, R.
  • Jiménez-Ramírez, O.
  • A. Quiroz-Juárez, M.
  • L. Aragón, J.

Abstract

This work shows and analyzes a system that produces arbitrary waveforms, which is a simplification, based on spatial discretization, of the BVAM model proposed by Barrio et al. in 1999 [1] to model the biological pattern formation. Since the analytical treatment of non-linear terms of this system is often prohibitive, its dynamic has been analyzed using a discrete equivalent system defined by a Poincaré map. In this analysis, the bifurcation diagrams and the Lyapunov exponent are the tools used to identify the different operating regimes of the system and to provide evidence of the periodicity and randomness of the generated waveforms. Also, it is shown that the analyzed system presents the period doubling phenomenon, the values of its bifurcation points are related by the Feigenbaum constant and they converge to the onset of chaos. It is shown that, the analyzed system can be electronically implemented using operational amplifiers to produce arbitrary waveforms when varying a single control parameter. The functionality and behavior of the ideal electronic implementation of the analyzed system is shown by the simulations obtained from the MatLab–Simulink™ toolbox. Finally, some problems related to a real electronic implementation are discussed. This paper gives a brief overview of how ideas from biology can be used to design new systems that produce arbitrary waveforms.

Suggested Citation

  • Vázquez-Medina, R. & Jiménez-Ramírez, O. & A. Quiroz-Juárez, M. & L. Aragón, J., 2013. "Arbitrary waveform generator biologically inspired," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 36-51.
    • Handle: RePEc:eee:chsofr:v:51:y:2013:i:c:p:36-51
    DOI: 10.1016/j.chaos.2013.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077913000465
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2013.03.006?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. Deborah A Striegel & Monica K Hurdal, 2009. "Chemically Based Mathematical Model for Development of Cerebral Cortical Folding Patterns," PLOS Computational Biology, Public Library of Science, vol. 5(9), pages 1-6, September.
    2. Cornejo-Pérez, O. & Solı´s-Perales, G.C. & Arenas-Prado, J.A., 2012. "Synchronization dynamics in a small pacemaker neuronal ensemble via a robust adaptive controller," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 861-868.
    3. Edwards, Roderick & Farcot, Etienne & Foxall, Eric, 2012. "Explicit construction of chaotic attractors in Glass networks," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 666-680.
    4. Quiroz, G. & Bonifas, I. & Barajas-Ramirez, J.G. & Femat, R., 2012. "Chaos evidence in catecholamine secretion at chromaffin cells," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 988-997.
    5. Zhou, Shangbo & Li, Hua & Zhu, Zhengzhou, 2008. "Chaos control and synchronization in a fractional neuron network system," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 973-984.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ledesma-Durán, Aldo & Aragón, José Luis, 2019. "Primary and secondary instabilities of the Mixed mode solution in a reaction diffusion system near the codimension-two Turing-Hopf point," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 68-77.

    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. Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Sun, Guoping & Yang, Feifei & Ren, Guodong & Wang, Chunni, 2023. "Energy encoding in a biophysical neuron and adaptive energy balance under field coupling," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Pham, Tuan D., 2014. "The butterfly effect in ER dynamics and ER-mitochondrial contacts," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 5-19.
    4. Zhang, Weiwei & Zhou, Shangbo & Li, Hua & Zhu, Hao, 2009. "Chaos in a fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1684-1691.
    5. Zhang, Jianlin & Bao, Han & Yu, Xihong & Chen, Bei, 2024. "Heterogeneous coexistence of extremely many attractors in adaptive synapse neuron considering memristive EMI," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    6. Das, Saptarshi & Pan, Indranil & Das, Shantanu, 2016. "Effect of random parameter switching on commensurate fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 157-173.
    7. Lin, Tsung-Chih & Lee, Tun-Yuan & Balas, Valentina E., 2011. "Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 791-801.
    8. Ismail, G.M. & Abdl-Rahim, H.R. & Abdel-Aty, A. & Kharabsheh, R. & Alharbi, W. & Abdel-Aty, M., 2020. "An analytical solution for fractional oscillator in a resisting medium," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    9. Julien Lefèvre & Jean-François Mangin, 2010. "A Reaction-Diffusion Model of Human Brain Development," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-10, April.
    10. Eshaghi, Shiva & Khoshsiar Ghaziani, Reza & Ansari, Alireza, 2020. "Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 321-340.
    11. Zhu, Hao & Zhou, Shangbo & He, Zhongshi, 2009. "Chaos synchronization of the fractional-order Chen’s system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2733-2740.
    12. Shahrear, Pabel & Glass, Leon & Wilds, Roy & Edwards, Rod, 2015. "Dynamics in piecewise linear and continuous models of complex switching networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 33-39.
    13. Ouannas, Adel & Khennaoui, Amina-Aicha & Odibat, Zaid & Pham, Viet-Thanh & Grassi, Giuseppe, 2019. "On the dynamics, control and synchronization of fractional-order Ikeda map," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 108-115.

    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:51:y:2013:i:c:p:36-51. 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.