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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 430963, 6 pages
Horseshoe Chaos in a 3D Neural Network with Different Activation Functions
1School of Optoelectronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Received 22 February 2013; Accepted 20 March 2013
Academic Editor: Xiao-Song Yang
Copyright © 2013 Fangyan Yang 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.
- M. R. Guevara, L. Glass, M. C. Mackey, and A. Shrier, “Chaos in neurobiology,” IEEE Transactions on Systems, Man and Cybernetics, vol. 13, no. 5, pp. 790–798, 1983.
- A. Babloyantz and C. Lourenço, “Brain chaos and computation,” International Journal of Neural Systems, vol. 7, no. 4, pp. 461–471, 1996.
- J. Guckenheimer and R. A. Oliva, “Chaos in the Hodgkin-Huxley model,” SIAM Journal on Applied Dynamical Systems, vol. 1, no. 1, pp. 105–114, 2002.
- J. E. Lewis and L. Glass, “Nonlinear dynamics and symbolic dynamics of neural networks,” Neural Computation, vol. 4, no. 5, pp. 621–642, 1992.
- R. Edwards, “Analysis of continuous-time switching networks,” Physica D, vol. 146, no. 1–4, pp. 165–199, 2000.
- H. Bersini and P. Sener, “The connections between the frustrated chaos and the intermittency chaos in small Hopfield networks,” Neural Networks, vol. 15, no. 10, pp. 1197–1204, 2002.
- Q. Li and X.-S. Yang, “Chaotic dynamics in a class of three dimensional Glass networks,” Chaos, vol. 16, no. 3, Article ID 033101, 5 pages, 2006.
- X.-S. Yang and Q. Li, “Chaos in simple cellular neural networks with connection matrices satisfying Dale's rule,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 17, no. 2, pp. 583–587, 2007.
- Q. Li, X. S. Yang, and F. Yang, “Hyperchaos in a simple CNN,” International Journal of Bifurcation and Chaos, vol. 16, no. 8, pp. 2453–2457, 2006.
- Q. Li and X. S. Yang, “Two kinds of horseshoes in a hyperchaotic neural network,” International Journal of Bifurcation and Chaos, vol. 22, no. 8, Article ID 1250200, 2012.
- L. Li and L. Chong-xin, “Application of chaos and neural network in power load forecasting,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 597634, 12 pages, 2011.
- T. Kanamaru and K. Aihara, “Rewiring-induced chaos in pulse-coupled neural networks,” Neural Computation, vol. 24, no. 4, pp. 1020–1046, 2012.
- M. A. Arbib, P. Erdi, and J. Szentagothai, Neural Organization: Structure, Function, and Dynamics, MIT Press, Cambridge, Mass, USA, 1997.
- F. Pasemann, “Complex dynamics and the structure of small neural networks,” Network, vol. 13, no. 2, pp. 195–216, 2002.
- A. Das, P. Das, and A. B. Roy, “Chaos in a three-dimensional general model of neural network,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 10, pp. 2271–2281, 2002.
- Q. Li and X. Yang, “Complex dynamics in a simple hopfield-type neural network,” in Advances in Neural Networks—ISNN 2005, vol. 3496 of Lecture Notes in Computer Science, pp. 357–362, Springer, Berlin, Germany, 2005.
- X. S. Yang and Y. Huang, “Complex dynamics in simple Hopfield neural networks,” Chaos, vol. 16, no. 3, Article ID 033114, 2006.
- Q. Yuan, Q. Li, and X.-S. Yang, “Horseshoe chaos in a class of simple Hopfield neural networks,” Chaos, Solitons and Fractals, vol. 39, no. 4, pp. 1522–1529, 2009.
- Z. H. Guan, F. Liu, J. Li, and T. Li, “A new chaotic hopfield neural network and its synthesis via parameter switchings,” Neurocomputing. In press.
- J. J. Hopfield, “Neurons with graded response have collective computational properties like those of two-state neurons,” Proceedings of the National Academy of Sciences of the United States of America, vol. 81, no. 10, pp. 3088–3092, 1984.
- Q. Li and X.-S. Yang, “A simple method for finding topological horseshoes,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 20, no. 2, pp. 467–478, 2010.
- Q. Li, L. Zhang, and F. Yang, “An algorithm to automatically detect the Smale horseshoes,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 283179, 9 pages, 2012.
- X.-S. Yang, “Topological horseshoes and computer assisted verification of chaotic dynamics,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 19, no. 4, pp. 1127–1145, 2009.
- X.-S. Yang and Y. Tang, “Horseshoes in piecewise continuous maps,” Chaos, Solitons and Fractals, vol. 19, no. 4, pp. 841–845, 2004.
- Q. Li, “A topological horseshoe in the hyperchaotic Rössler attractor,” Physics Letters A, vol. 372, no. 17, pp. 2989–2994, 2008.
- C. Lia, L. Wub, H. Lic, and Y. Tongc, “A novel chaotic system and its topological horseshoe,” Nonlinear Analysis, vol. 18, no. 1, pp. 66–77, 2013.
- Q.-j. Fan, “Horseshoe in a modified Van der Pol-Duffing circuit,” Applied Mathematics and Computation, vol. 210, no. 2, pp. 436–440, 2009.
- Q. Li and X.-S. Yang, “New walking dynamics in the simplest passive bipedal walking model,” Applied Mathematical Modelling, vol. 36, no. 11, pp. 5262–5271, 2012.
- Q. Fan, “Horseshoe chaos in a hybrid planar dynamical system,” International Journal of Bifurcation and Chaos, vol. 22, no. 8, Article ID 1250202, 2012.
- Q. D. Li, S. Chen, and P. Zhou, “Horseshoe and entropy in a fractional-order unified system,” Chinese Physics B, vol. 20, no. 1, Article ID 010502, 2011.
- Q. Li, X. S. Yang, and S. Chen, “Hyperchaos in a spacecraft power system,” International Journal of Bifurcation and Chaos, vol. 21, no. 6, pp. 1719–1726, 2011.