- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 318758, 11 pages
Single Gaussian Chaotic Neuron: Numerical Study and Implementation in an Embedded System
Universidad Autónoma de Nuevo León, UANL, FIME, Avenida Universidad S/N Ciudad Universitaria, 66451 San Nicolás de los Garza Nuevo León, NL, Mexico
Received 26 October 2012; Revised 28 December 2012; Accepted 3 January 2013
Academic Editor: Eric Campos Canton
Copyright © 2013 Luis M. Torres-Treviño et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- K. Aihara, G. Matsumoto, and Y. Ikegaya, “Periodic and nonperiodic responses of a periodically forced Hodgkin-Huxley oscillator,” Journal of Theoretical Biology, vol. 109, no. 2, pp. 249–269, 1984.
- W. Wang, “Bifurcations and chaos of the Bonhoeffer-van der Pol model,” Journal of Physics A, vol. 22, no. 13, pp. L627–L632, 1989.
- H. Korn and P. Faure, “Is there chaos in the brain? II. Experimental evidence and related models,” Comptes Rendus, vol. 326, no. 9, pp. 787–840, 2003.
- D. C. Soriano, F. I. Fazanaro, R. Suyama, J. R. de Oliveira, R. Attux, and M. K. Madrid, “A method for Lyapunov spectrum estimation using cloned dynamics and its application to the discontinuously-excited Fitzhugh-Nagumo model,” Nonlinear Dynamics, vol. 67, pp. 413–424, 2012.
- C. Li and G. Chen, “Coexisting chaotic attractors in a single neuron model with adapting feedback synapse,” Chaos, Solitons & Fractals, vol. 23, no. 5, pp. 1599–1604, 2005.
- N. Sungar, E. Allaria, I. Leyva, and F. T. Arecchi, “Comparison of single neuron models in terms of synchronization propensity,” Chaos, vol. 18, no. 3, article 033108, 2008.
- S. El Boustani and A. Destexhe, “Brain dynamics at multiple scales: can one reconcile the apparent low-dimensional chaos of macroscopic variables with the seemingly stochastic behavior of single neurons?” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 20, no. 6, pp. 1687–1702, 2010.
- J. Laudanski, C. Sumner, and S. Coombes, “Calcium window currents, periodic forcing, and chaos: understanding single neuron response with a discontinuous one-dimensional map,” Physical Review E, vol. 82, no. 1, article 011924, p. 9, 2010.
- V. I. Sbitnev and L. O. Chua, “Local activity criteria for discrete-map CNN,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 6, pp. 1227–1272, 2002.
- T. Roska and L. O. Chua, “The CNN Universal Machine: 10 years later,” Journal of Circuits, Systems and Computers, vol. 12, no. 4, pp. 377–388, 2003.
- H. Xing, L. Chuandong, and S. Yonglu, “Bogdanov-takens bifurcation in a single inertial neuron model with delay,” Neurocomputing, vol. 89, pp. 193–201, 2012.
- E. Campos-Canton, R. Femat, and G. Chen, “Attractors generated from switching unstable dissipative systems,” Chaos, vol. 22, Article ID 033121, 2012.
- E. Campos-Cantón, J. G. Barajas-Ramírez, G. Solís-Perales, and R. Femat, “Multiscroll attractors by switching systems,” Chaos, vol. 20, no. 1, article 013116, 2010.
- J. Chen and C. G. Li, “Circuit design of tabu learning neuron models and their dynamic behavior,” Acta Physica Sinica, vol. 60, no. 2, Article ID 020502, 2011.
- I. Campos-Cantón, E. Campos-Cantón, and E. Castellanos-Velasco, “Signal generator based on a chaotic circuit,” Analog Integrated Circuits and Signal Processing, vol. 66, no. 2, pp. 309–313, 2011.
- J. Kim and J. Jung, “Fully integrated circuit design aiharas chaotic neuron model,” in IEEE Conference Publications, pp. 258–259, 2010.
- D. D. Gajski and F. Vahid, “Specification and design of embedded hardware-software systems,” IEEE Design and Test of Computers, vol. 12, no. 1, pp. 53–67, 1995.
- F. Balarin, M. Chiodo, and P. Giusto, Hardware-Software Co-Design of Embedded Systems, Kluwer Academic Publishers, 1997.
- D. Cuartielles and M. Banzi, “Arduino official web page,” 2012, http://www.arduino.cc/.
- S. Haykin, Neural Networks and Learning Machines, Pearson, 2008.
- S. H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press, 2000.
- S. Lynch, Dynamical Systems with Applications Using Mapple, Springer-Birkhuser, 2010.
- F. C. Moon, Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers, Wiley-VCH, 2004.
- A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D, vol. 16, no. 3, pp. 285–317, 1985.