Multiple μ-stability of neural networks with unbounded time-varying delays

Neural Networks

Volumn 53, Issue , 2014, Pages 109-118

  Wang, Lili ^a   Chen, Tianping ^b  

^a SHANGHAI UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^b FUDAN UNIVERSITY   (China)

Author keywords

stability; Multistability; Neural networks; Nonlinear activation function; Unbounded delays

Indexed keywords

ACTIVATION FUNCTIONS; EQUILIBRIUM POINT; GEOMETRICAL CONFIGURATIONS; MATHEMATICAL ANALYSIS; MULTI STABILITIES; NONLINEAR ACTIVATION FUNCTIONS; TIME-VARYING DELAY; UNBOUNDED DELAYS;

NEURAL NETWORKS; PHASE SPACE METHODS; RECURRENT NEURAL NETWORKS;

STABILITY CRITERIA;

ARTICLE; ARTIFICIAL NEURAL NETWORK; EQUILIBRIUM CONSTANT; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; NONLINEAR SYSTEM; PRIORITY JOURNAL; SIMULATION; UNBOUNDED TIME VARYING DELAY; ALGORITHM; COMPUTER SIMULATION; TIME;

ALGORITHMS; COMPUTER SIMULATION; NEURAL NETWORKS (COMPUTER); TIME FACTORS;

EID: 84896839707     PISSN: 08936080     EISSN: 18792782     Source Type: Journal    
DOI: 10.1016/j.neunet.2014.02.001     Document Type: Article

References (25)

1. Angeli D. Convergence in networks with counterclockwise neural dynamics. IEEE Transactions on Neural Networks 2009, 20(5):794-804.
2. Chen T., Wang L. Power-rate global stability of dynamical systems with unbounded time-varying delays. IEEE Transactions on Circuits and Systems II: Express Briefs 2007, 54(8):705-709.
3. Chen T., Wang L. Global μ-stability of delayed neural networks with unbounded time-varying delays. IEEE Transactions on Neural Networks 2007, 18(6):1836-1840.
4. Cheng C., Lin K., Shih C. Multistability in recurrent neural networks. SIAM Journal on Applied Mathematics 2006, 66(4):1301-1320.
5. Cheng C., Shih C. Complete stability in multistable delayed neural networks. Neural Computation 2009, 21:719-740.
6. Di Marco M., Forti M., Grazzini M., Pancioni L. Limit set dichotomy and convergence of cooperative piecewise linear neural networks. IEEE Transactions on Circuits and Systems I 2011, 58(5):1052-1062.
7. Di Marco M., Forti M., Grazzini M., Pancioni L. Limit set dichotomy and multistability for a class of cooperative neural networks with delays. IEEE Transactions on Neural Networks and Learning Systems 2012, 23(9):1473-1485.
8. Fang Y., Kincaid T.G. Global properties for a class of dynamical neural circuits. Journal of the Franklin Institute 1998, 335(1):163-177.
9. Gershman S.J., Vul E., Tenenbaum J. Multistability and perceptual inference. Neural Computation 2012, 24:1-24.
10. Hopfield J.J. Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences 1984, 81:3088-3092.
11. Huang Y., Zhang H., Wang Z. Dynamical stability analysis of multiple equilibrium points in time-varying delayed recurrent neural networks with discontinuous activation functions. Neurocomputing 2012, 91:21-28.
12. Kaslik E., Sivasundaram S. Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis. Neural Networks 2011, 24(4):370-377.
13. Kelso J.A. Multistability and metastability: understanding dynamic coordination in the brain. Philosophical Transactions of the Royal Society, Series B 2012, 367:906-918.
14. Li J.H., Michel A.N., Porod W. Qualitative analysis and synthesis of a class of neural networks. IEEE Transactions on Circuits and Systems 1988, 35(8):976-986.
15. Lu W., Wang J. Convergence analysis of a class of nonsmooth gradient systems. IEEE Transactions on Circuits and Systems I 2008, 55(11):3514-3527.
16. Lu W., Wang L., Chen T. On attracting basins of multiple equilibria of a class of cellular neural networks. IEEE Transactions on Neural Networks 2011, 22(3):381-394.
17. Nie X., Huang Z. Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions. Neurocomputing 2012, 82:1-13.
18. Wang L. Dynamical analysis on the multistability of high-order neural networks. Neurocomputing 2013, 110:137-144.
19. Wang L., Chen T. Multistability of neural networks with Mexican-hat-type activation functions. IEEE Transactions on Neural Networks and Learning Systems 2012, 23(11):1816-1826.
20. Wang L., Chen T. Complete stability of cellular neural networks with unbounded time-varying delays. Neural Networks 2012, 36:11-17.
21. Wang L., Lu W., Chen T. Multistability and new attraction basins of almost-periodic solutions of delayed neural networks. IEEE Transactions on Neural Networks 2009, 20(10):1581-1593.
22. Wang L., Lu W., Chen T. Coexistence and local stability of multiple equilibria in neural networks with piecewise linear nondecreasing activation functions. Neural Networks 2010, 23:189-200.
23. Zeng Z., Huang T., Zheng W. Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function. IEEE Transactions on Neural Networks 2010, 21(8):1371-1377.
24. Zeng Z., Wang J. Multiperiodicity and exponential attractivity evoked by periodic external inputs in delayed cellular neural networks. Neural Computation 2006, 18:848-870.
25. Zhang L., Yi Z., Yu J., Heng P. Some multistability properties of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions. Neurocomputing 2009, 72:3809-3817.