Convergence analysis of general neural networks under almost periodic stimuli

International Journal of Circuit Theory and Applications

Volumn 37, Issue 6, 2009, Pages 723-750

  Huang, Zhenkun ^a,b   Mohamad, S ^b   Wang, Xinghua ^c   Feng, Chunhua ^d  

^a JIMEI UNIVERSITY   (China)

^b UNIVERSITI BRUNEI DARUSSALAM   (Brunei Darussalam)

^c ZHEJIANG UNIVERSITY   (China)

^d GUANGXI NORMAL UNIVERSITY   (China)

Author keywords

Almost periodic; Attracting basins; Encoded patterns; Exponential stability; Neural networks

Indexed keywords

ASYMPTOTIC STABILITY; MAGNETIC MATERIALS; NEURAL NETWORKS;

ACTIVATION FUNCTIONS; ALMOST PERIODIC; ATTRACTING BASINS; CONVERGENCE ANALYSIS; ENCODED PATTERNS; INEQUALITY TECHNIQUES; INVARIANT REGIONS;

CIRCUIT THEORY;

EID: 68149136318     PISSN: 00989886     EISSN: 1097007X     Source Type: Journal    
DOI: 10.1002/cta.490     Document Type: Article

References (57)

1. Chua LO, Yang L. Cellular neural networks: theory. IEEE Transactions on Circuits and Systems 1988; 35: 1257-1272.
2. Chua LO, Yang L. Cellular neural networks: application. IEEE Transactions on Circuits and Systems 1988; 35:1273-1290.
3. Foss J, Longtin A, Mensour B, Milton J. Multistability and delayed recurrent loops. Physical Review Letters 1996; 76:708-711.
4. Hopfield J. 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 1984; 81:3088-3092.
5. Forti F. On global asymptotic stability of a class of nonlinear systems arising in neural network theory. Journal of Differential Equations 1994; 113:246-264.
6. Cheng CY, Lin KH, Shih CW. Multistability in recurrent neural networks. SIAM Journal on Applied Mathematics 2006; 66(4):1301-1320.
7. Zeng Z, Huang DS, Wang Z. Memory pattern analysis of cellular neural networks. Physics Letters A 2005; 342:114-128.
8. Cheng CY, Lin KH, Shih CW. Multistability and convergence in delayed neural networks. Physica D 2007; 225:61-74.
9. Shayer LP, Campbell SA. Stability, bifurcation and multistability in a system of two coupled neurons with multiple time delays. SIAM Journal on Applied Mathematics 2000; 61:673-700.
10. Takhashi N. A new sufficient condition for complete stability of cellular neural networks with delay. IEEE Transactions on Circuits and Systems I 2000; 47(6):793-799.
11. Feng C, Plamondon R. On the stability analysis of delayed neural networks systems. Neural Networks 2001; 14:1181-1188.
12. Lu KN, Xu DY, Yang ZC. Global attraction and stability for Cohen-Grossberg neural networks with delays. Neural Networks 2006. DOI: 10.1016j.neunet.2006.07.006.
13. Gopalsamy K, He XZ. Delay-independent stability in bi-directional associative memory networks. IEEE Transactions on Neural Networks 1994; 5:998-1002.
14. Liao XF, Yu JB. Qualitative analysis of bidirectional associative memory with time delays. International Journal of Circuit Theory and Applications 1998; 26:219-229.
15. Petras I, Gilli M. Complex dynamics in one-dimensional cellular neural networks. International Journal of Circuit Theory and Applications 2006; 34:3-20.
16. Carbone A, Palma F. Discontinuity correction in piecewise-linear models of oscillators for phase noise characterization. International Journal of Circuit Theory and Applications 2007; 35(1):93-104.
17. Forti M. M-matrices and global convergence of discontinuous neural networks. International Journal of Circuit Theory and Applications 2007; 35(2):105-130.
18. Huang ZK, Li X, Mohamod S, Lu Z. Robust stability analysis of static neural network with S-type distributed delays. Applied Mathematical Modelling 2007. DOI: 10.1016j.apm.2007.12.006.
19. Demir A. Fully nonlinear oscillator noise analysis: an oscillator with no asymptotic phase. International Journal of Circuit Theory and Applications 2007; 35(2):175-203.
20. Huang ZK, Xia Y. Exponential p-stability of second order Cohen-Grossberg neural networks with transmission delays and learning behavior. Simulation Modelling Practice and Theory 2007; 15:622-634.
21. Gilli M. Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions. IEEE Transactions on Circuits and Systems I 1994; 41:518-528.
22. Gilli M. Analysis of periodic oscillations in finite-dimensional CNNs through a spatio-temporal harmonic balance technique. International Journal of Circuit Theory and Applications 1998; 25(4):279-288.
23. Lanza V, Corinto F, Gilli M, Civalleri PP. Analysis of nonlinear oscillatory network dynamics via time-varying amplitude and phase variables. International Journal of Circuit Theory and Applications 2007; 35(5-6):623-644.
24. Civalleri PP, Gilli M, Bonnin M. Equivalent circuits for small signal performance of spin 1/2 particles. International Journal of Circuit Theory and Applications 2006; 34(2):165-182.
25. Petrás I, Gilli M. Complex dynamics in one-dimensional CNNs. International Journal of Circuit Theory and Applications 2006; 34(1):3-20.
26. Forti M. M-matrices and global convergence of discontinuous neural networks. International Journal of Circuit Theory and Applications 2007; 35(2):105-130.
27. Huang ZK, Xia YH, Wang XH. Exponential stability of impulsive Cohen-Grossberg networks with distributed delays. International Journal of Circuit Theory and Applications, in press. DOI: 10.1002/cta.424.
28. Mohamad S. Convergence dynamics of delayed Hopfield-type neural networks under almost periodic stimuli. Acta Applicandae Mathematicae 2003; 76:117-135.
29. Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic Publishers: The Netherlands, 1992.
30. Fink AM. Almost Periodic Differential Equations. Springer: New York, 1974.
31. He CY. Almost Periodic Differential Equations. Higher Education: Beijing, China, 1992.
32. Lu WL, Chen TP. Global stability of almost periodic solution for delayed neural networks. Chinese Science A 2005; 35(7):774-784.
33. Feng C, Wang P. Almost periodic solutions of forced Lienard-type equations with time delays. Journal of Computational and Applied Mathematics 2003; 161:p.
34. Huang ZK, Wang XH, Gao F. The existence and global attractivity of almost periodic sequence solution of discrete-time neural networks. Physics Letters A 2006; 350:182-191.
35. Huang ZK, Xia YH, Wang XH. The existence and exponential attractivity of -almost periodic sequence solution of discrete time neural networks. Nonlinear Dynamics 2007; 50:13-26.
36. Liu BW, Huang LH. Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays. Physics Letters A 2005; 341:135-144.
37. Zhao HY. Existence and global exponential convergence of almost periodic solutions for cellular neural networks with variable delay. Journal of Engineering Mathematics 2005; 22(2):295-300.
38. Zhao HY, Wang GL. Existence and global attractivity of almost periodic solutions for Hopfield neural networks with variable delay. Acta Mathematica Scientia 2004; 24(6):723-729.
39. Chen AP, Huang LH. Existence and attractivity of almost periodic solutions of Hopfield neural networks. Acta Mathematica Scientia 2001; 21(4):505-511.
40. Huang H, Ho DWC, Cao JD. Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays. Neural Networks 2005; 18:161-170. (Pubitemid 40431614)
41. Cao JD, Li Q. On the exponential stability and periodic solutions of delayed cellular neural networks. Journal of Mathematical Analysis and Applications 2000; 252:50-64.
42. Fang H, Li JB. Global exponential stability and periodic solutions of cellular neural networks with delay. Physical Review E 2000; 61(4):4212-4217.
43. Cao JD. Periodic solutions and exponential stability in delayed cellular neural networks. Physical Review E 1999; 60(3):3244-3248.
44. Cao JD, Wang L. Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Transactions on Neural Networks 2002; 13:457-463.
45. Song QK, Wang ZD. An analysis on existence and global exponential stability of periodic solutions for BAM neural networks with time-varying delays. Nonlinear Analysis: Real World Applications 2006. DOI: 10.1016/j.nonrwa.2006.07.002.
46. Chen AP, Huang LH, Liu ZG, Cao JD. Periodic bidirectional associative memory neural networks with distributed delays. Journal of Mathematical Analysis and Applications 2006; 317:80-102.
47. Jiang HJ, Teng ZD. Dynamics of neural networks with variable coefficients and time-varying delays. Neural Networks 2006; 19:676-683.
48. Huang LH, Huang CX, Liu BW. Dynamics of a class of cellular neural networks with time-varying delays. Physics Letters A 2005; 345:330-344.
49. Liu YG, You ZS, Cao LP. On the almost periodic solution of cellular neural networks with distributed delays. IEEE Transactions on Neural Networks 2007; 18:295-300.
50. Guo SJ, Huang LH. Exponential stability and periodic solutions of neural networks with continuously distributed delays. Physical Review E 2003; 67:011902.
51. Berman A, Plemmons RJ. Nonnegative Matrices in the Mathematical Science. Academic Press: New York, 1929.
52. Horn RA, Johnson CR. Topics in Matrix Analysis. Cambridge University Press: Cambridge, U. K., 1991.
53. Roska T, Chua LO. Cellular neural networks with non-linear and delay-type template elements and non-uniform grids. International Journal of Circuit Theory and Applications 1992; 20:469-481.
54. Brucoli M, Carnimeo L, Grassi G. Discrete-time cellular neural networks for associative memories with learning and forgetting capabilities. IEEE Transactions on Circuits and Systems I 1995; 42(7):396-399.
55. Juang J, Lin SS. Cellular neural networks: mosaic pattern and spatial chaos. SIAM Journal on Applied Mathematics 2000; 60:891-915.
56. Shih CW. Pattern formation and spatial chaos for cellular neural networks with asymmetric templates. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1998; 8:1907-1936.
57. Shih CW. Influence of boundary conditions on pattern formation and spatial chaos in lattice systems. SIAM Journal on Applied Mathematics 2000; 61:335-368.