Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations

Applied Mathematical Modelling

Volumn 33, Issue 12, 2009, Pages 4326-4336

  Li, Liping ^a,b   Huang, Lihong ^a  

^a HUNAN UNIVERSITY   (China)

^b HUZHOU UNIVERSITY   (China)

Author keywords

Differential inclusion; Discontinuous recurrent neural network; Filippov solution; Global exponential stability; M matrix

Indexed keywords

DIFFERENTIAL INCLUSION; DISCONTINUOUS RECURRENT NEURAL NETWORK; FILIPPOV SOLUTION; GLOBAL EXPONENTIAL STABILITY; M-MATRIX;

CHEMICAL ACTIVATION; DIFFERENTIAL EQUATIONS; REINFORCEMENT LEARNING; SYSTEM STABILITY; TIME VARYING NETWORKS;

RECURRENT NEURAL NETWORKS;

EID: 68049124938     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2009.03.014     Document Type: Article

References (34)

1. Grossberg S. Nonlinear neural networks: principles mechanisms and architectures. Neural Networks 1 (1988) 17-61
2. Hirsch M.W. Convergent activation dynamics in continuous time networks. Neural Networks 2 (1989) 331-349
3. Avitabile G., Forti M., Manetti S., and Marini M. On a class of nonsymmetrical neural networks with application to ADC. IEEE Trans. Circuits Syst. 38 (1991) 202-209
4. Liang X., and Wang J. A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints. IEEE Trans. Neural Networks 11 (2000) 1251-1262
5. Forti M., Manetti S., and Marini M. A condition for global convergence of a class of symmetric neural networks. IEEE Trans. Circuits Syst. I 39 (1992) 480-483
6. Hu S., and Wang J. Global stability of a class of continuous-time recurrent neural networks. IEEE Trans. Circuits Syst. I 49 (2002) 1334-1347
7. Xia Y., and Wang J. Global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weight weights. IEEE Trans. Automat. Contr. 46 (2001) 635-638
8. Qiao H., Peng J., Xu Z., and Zhang B. A reference model approach to stability analysis of neural networks. IEEE Trans. Circuits Syst. I 50 (2003) 925-936
9. Guo S., and Huang L. Stability analysis of Cohen-Grossberg neural networks. IEEE Trans. Neural Networks 17 (2006) 106-117
10. Forti M., Manetti S., and Marini M. Necessary and sufficient condition for absolute stability of neural networks. IEEE Trans. Circuits Syst. 41 (1994) 491-494
11. Kaszkurewicz E., and Bhaya A. On a class of globally stable neural circuits. IEEE Trans. Circuits Syst. I 41 (1994) 171-174
12. Kelly D. Stability in contractive nonlinear neural networks. IEEE Trans. Biomed. Eng. 3 (1990) 231-242
13. Matsuoka K. Stability condition for nonlinear neural networks with asymmetric connection weight. Neural Networks 5 (1992) 495-500
14. Morita M. Associative memory with nonmonotone dynamics. Neural Networks 6 (1993) 115-126
15. Forti M. On global asymptotic stability of a class of nonlinear arising in neural networks theory. J. Differ. Equations 113 (1994) 246-264
16. Forti M., and Tesi A. New condition for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans. Circuits Syst. I 42 (1995) 354-366
17. Liang X. A comment on equilibria, stability, and instability of Hopfield neural networks. IEEE Trans. Neural Networks 11 (2000) 1506-1507
18. Kaszkurewicz E., and Bhaya A. Comments on necessary and sufficient condition for absolute stability of neural networks. IEEE Trans. Circuits Syst. I 42 (1995) 497-499
19. Kennedy M.P., and Chua L.O. Neural networks for nonlinear programming. IEEE Trans. Circuits Syst. I 35 (1988) 554-562
20. Forti M., and Nistri P. Global convergence of neural networks with discontinuous neuron activations. IEEE Trans. Circuits Syst. I 50 (2003) 1421-1435
21. Forti M., Grazzini M., Nistri P., and Pancioni L. Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Phys. D 214 (2006) 88-99
22. Forti M. M-matrices and global convergence of discontinuous neural networks. Int. J. Circuit Theor. Appl. 35 (2007) 105C130
23. Lu W., and Chen T. Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions. Neural Networks 18 (2005) 231-242
24. Forti M., Nistri P., and Papini D. Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans. Neural Networks 16 (2005) 1449-1463
25. Lu W., and Chen T. Dynamical behaviors of delayed neural network systems with discontinuous activations functions. Neural Comput. 18 (2006) 683-708
26. Song Q. Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach. Neurocomputing 71 (2008) 2823-2830
27. Aubin J.P., and Frankowska H. Set-Valued Analysis (1990), Birkhäuser, Boston
28. Bhaya A., Kaszkurewicz E., and Santos R. Characterizations of classes of stable matrices. Linear Algebra Appl. 374 (2003) 159-174
29. Filippov A.F. Differential Equations with Discontinuous Righthand Side. Mathematics and Its Applications (Soviet Series) (1988), Kluwer Academic, Boston, MA
30. Fiedler M., and Pdak V. some generalization of positive definiteness and monotonicity. Numer. Math. 9 (1966) 162-173
31. Aubin J.P., and Cellina A. Differential Inclusions (1984), Springer-Verlag, Berlin
32. Hale J.K. Ordinary Differential Equations (1969), Wiley, New York
33. Clarke F.H. Optimization and Non-smooth Analysis (1983), Wiley, New York
34. Baiotti A., Conti R., and Marcellini P. Discontinuous Ordinary Differential Equations and Stabilization (2000), Universita di Firenze