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Arbitrary waveform generator biologically inspired

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  • 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
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    References listed on IDEAS

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    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. 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.
    5. 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.
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    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.

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