Scale-limited activating sets and multiperiodicity for threshold-linear networks on time scales

IEEE Transactions on Cybernetics

Volumn 44, Issue 4, 2014, Pages 488-499

  Huang, Zhenkun ^a   Raffoul, Youssef N ^b   Cheng, Chang Yuan ^c  

^a JIMEI UNIVERSITY   (China)

^b UNIVERSITY OF DAYTON   (United States)

^c NATIONAL PINGTUNG UNIVERSITY   (Taiwan)

Author keywords

Multiperiodicity; scale limited activating set; threshold linear network; time scale

Indexed keywords

COMPUTER SIMULATION; TIME MEASUREMENT;

DYNAMICAL PROPERTIES; GLOBAL ATTRACTIVITY; MULTIPERIODICITY; NONDIVERGENCE; SCALE-LIMITED ACTIVATING SET; SELF EXCITATION; TIME EVOLUTIONS; TIME-SCALES;

LINEAR NETWORKS;

EID: 84896910470     PISSN: 21682267     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCYB.2013.2257747     Document Type: Article

References (21)

1. L. O. Chua and L. Yang, "Cellular neural networks: Application," IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1273-1290, Oct. 1988.
2. R. Douglas, C. Koch, M. Mahowald, K. Martin, and H. Suarez, "Recurrent excitation in neocortical circuits," Science, vol. 269, no. 5226, pp. 981-985, 1995.
3. R. H. R. Hahnloser, R. Sarpeshkar, M. A. Mahowald, R. J. Douglas, and H. S. Seung, "Digital selection and analogue amplification coexist in a cortexinspired silicon circuit," Nature, vol. 405, pp. 947-951, Jun. 2000. (Pubitemid 30435050)
4. H. J. Tang, K. C. Tan, and E. J. Teoh, "Dynamics analysis and analog associative memory of networks with LT neurons," IEEE Trans. Neural Netw., vol. 17, no. 2, pp. 409-418, Mar. 2006. (Pubitemid 43380064)
5. Z. Yi and K. K. Tan, "Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions," IEEE Trans. Neural Netw., vol. 15, no. 2, pp. 329-336, Mar. 2004.
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. (Pubitemid 37049820)
7. Z. Zeng and J. Wang, "Multiperiodicity of discrete-time delayed neural networks evoked by periodic external inputs," IEEE Trans. Neural Netw., vol. 17, no. 5, pp. 1141-1151, Sep. 2006. (Pubitemid 46445173)
8. Z. Zeng and J. Wang, "Multiperiodicity and exponential attractivity evoked by periodic external inputs in delayed cellular neural networks," Neural Comput., vol. 18, no. 4, pp. 848-870, 2006. (Pubitemid 43543824)
9. 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. (Pubitemid 351279234)
10. C. Cheng, K. Lin, and C. Shih, "Multistability in recurrent neural networks," SIAM J. Appl. Math., vol. 66, no. 4, pp. 1301-1320, 2006. (Pubitemid 44231191)
11. C. Cheng, K. Lin, and C. Shih, "Multistability and convergence in delayed neural networks," Physica D, vol. 225, no. 1, pp. 61-74, 2007. (Pubitemid 44854234)
12. S. Mohamad, "Exponential stability preservation in discrete-time analogues of artificial neural networks with distributed delays," J. Comput. Appl. Math., vol. 215, no. 1, pp. 270-287, 2008. (Pubitemid 351324856)
13. S. Hu and J. Wang, "Global stability of a class of discrete-time recurrent neural networks," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 8, pp. 1104-1117, Aug. 2002. (Pubitemid 34974184)
14. L. P. Shayer and S. A. Campell, "Stability, bifurcation and multistability in a system of two coupled neurons with multiple time delays," SIAM J. Appl. Math., vol. 61, no. 2, pp. 673-700, 2000. (Pubitemid 32456327)
15. Z. Huang, S. Mohamad, X. Wang, and C. H. Feng, "Convergence analysis of general neural networks under almost periodic stimuli," Int. J. Circ. Theor. Appl., vol. 37, no. 6, pp. 723-750, 2009.
16. L. Wang, W. Lu, and T. Chen, "Coexistence and local stability of multiple equilibria in neural networks with piecewise linear nondecreasing activation functions," Neural Netw., vol. 23, no. 2, pp. 189-200, 2010.
17. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Boston, MA, USA: Birkhauser, 2001.
18. 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, no. 8, pp. 1811-1825, 2001. (Pubitemid 33594317)
19. K. C. Tan, H. J. Tang, and W. N. Zhang, "Qualitative analysis for recurrent neural networks with linear threshold transfer functions," IEEE Trans. Circuits Syst., vol. 52, no. 5, pp. 1003-1012, May 2005. (Pubitemid 40773626)
20. H. J. Tang, K. C. Tan, and W. N. Zhang, "Analysis of cyclic dynamics for networks of linear threshold neurons," Neural Comput., vol. 17, no. 1, pp. 97-114, 2005. (Pubitemid 40305884)
21. E. R. Kaufmann and Y. N. Raffoul, "Periodic solutions for a neutral nonlinear dynamical equation on a time scale," J. Math. Anl. Appl., vol. 319, pp. 315-325, 2006. (Pubitemid 43506862)