TY - JOUR
T1 - Arbitrary waveform generator biologically inspired
AU - Vázquez-Medina, R.
AU - Jiménez-Ramírez, O.
AU - A. Quiroz-Juárez, M.
AU - L. Aragón, J.
N1 - Funding Information:
Technical, computational, support from Beatriz Millán and Alejandro Gómez is gratefully acknowledged. RVM thanks financial support of SIP IPN 20130461, ICYTDF/270/2010 and ICYTDF/325/2011 projects, and for the research support of Departamento de Nanotecnología, Centro de Física Aplicada y Tecnología Avanzada, UNAM Campus Querétaro, México. JLA wants to acknowledge financial support by CONACyT and DGAPA-UNAM, México, under grants 167244 and IN100310-3, respectively. The authors acknowledge the support of the IPN for the patent application process.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84876242325&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2013.03.006
DO - 10.1016/j.chaos.2013.03.006
M3 - Artículo
SN - 0960-0779
VL - 51
SP - 36
EP - 51
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
ER -