Analysis of continuous attractors for 2-D linear threshold neural networks

IEEE Transactions on Neural Networks

Volumn 20, Issue 1, 2009, Pages 175-180

  Zou, Lan ^a   Tang, Huajin ^b   Tan, Kay Chen ^c   Zhang, Weinian ^a  

^a SICHUAN UNIVERSITY   (China)

^b INSTITUTE FOR INFOCOMM RESEARCH   (Singapore)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Continuous attractor; Degenerate equilibria; Linear threshold (LT) network; Multistable neural network; Singular line

Indexed keywords

CONTINUOUS ATTRACTOR; DEGENERATE EQUILIBRIA; LINEAR THRESHOLD (LT) NETWORK; MULTISTABLE NEURAL NETWORK; SINGULAR LINE;

NEURAL NETWORKS;

ALGORITHM; ANIMAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; COMPUTER SIMULATION; FEEDBACK SYSTEM; NERVE TRACT; PHYSIOLOGY; STATISTICAL MODEL; VISUAL CORTEX;

ALGORITHMS; ANIMALS; COMPUTER SIMULATION; FEEDBACK; LINEAR MODELS; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); NEURAL PATHWAYS; VISUAL CORTEX;

EID: 58649120510     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2008.2009535     Document Type: Article

References (15)

1. R. L. T. Hahnloser, "On the piecewise analysis of linear threshold neural networks," Neural Netw., vol. 11, pp. 691-697, 1998.
2. R. Douglas, C. Koch, M. Mahowald, and H. Suarez, "Recurrent excitation in neocortical circuits," Science, vol. 269, pp. 981-985, 1995.
3. H. Wersing, W.-J. Beyn, and H. Ritter, "Dynamical stability conditions for recurrent neural networks with unsaturating piecewise linear transfer functions," Neural Comput., vol. 13, pp. 1811-1825, 2001.
4. R. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, "Digital selection and analogue amplification coexist in a cortex-inspired silicon circuits," Nature, vol. 405, pp. 947-951, 2000.
5. H. S. Seung, "Continuous attractors and oculomotor control," Science, vol. 290, pp. 2268-2269, 2000.
6. Z. Yi, K. K. Tan, and T. H. Lee, "Multistability analysis for recurrent neural networks with unsaturating piecewise linear transfer functions," Neural Comput., vol. 15, no. 3, pp. 639-662, 2003.
7. L. Zhang, Z. Yi, and J. Yu, "Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions," IEEE Trans. Neural Netw., vol. 19, no. 1, pp. 158-167, Jan. 2008.
8. A. Meyer-Base and V. Thummler, "Local and global stability analysis of an unsupervised competitive neural network," IEEE Trans. Neural Netw., vol. 19, no. 2, pp. 346-351, Feb. 2008.
9. A. A. Frolov, D. Husek, I. P. Muraviev, and P. Y. Polyakov, "Boolean factor analysis by attractor neural network," IEEE Trans. Neural Netw., vol. 18, no. 3, pp. 698-707, May 2007.
10. Z.-H. Mao and S. G. Massaquoi, "Dynamics of winner-take-all competition in recurrent neural networks with lateral inhibition," IEEE Trans. Neural Netw., vol. 18, no. 1, pp. 55-69, Jan. 2007.
11. K. C. Tan, H. Tang, and W. Zhang, "Qualitative analysis for recurrent neural networks with linear threshold transfer functions," IEEE Trans. Circuit Syst. I, Reg. Papers, vol. 52, no. 5, pp. 1003-1012, May 2005.
12. H. S. Seung, "How the brain keeps the eyes still," Proc. Nat. Acad. Sci. USA, vol. 93, pp. 13339-13344, 1996.
13. H. Tang, K. C. Tan, and W. Zhang, "Cyclic dynamics analysis for networks of linear threshold neurons," Neural Comput., vol. 17, no. 1, pp. 97-114, 2005.
14. Z.-F. Zhang, T.-R. Ding, W.-Z. Huang, and Z.-X. Dong, Qualitative Theory of Differential Equations. Providence, RI: Transl. Math. Monographs, Amer. Math. Soc., 1992.
15. J. Milton, "EPILESPY: Multistability in a dynamic disease," in Self-Organized Biological Dynamics Nonlinear Control: Toward Understanding Complexity, Chaos, and Emergent Function in Living Systems J. Walleczek, Ed. Cambridge, U.K.: Cambridge Univ. Press, 2000, pp. 374-386.