Global asymptotic stability of neural networks with discontinuous activations

Neural Networks

Volumn 22, Issue 7, 2009, Pages 931-937

  Wang, Jiafu ^a   Huang, Lihong ^a   Guo, Zhenyuan ^a  

^a HUNAN UNIVERSITY   (China)

Author keywords

Convergence in finite time; Differential inclusion; Discontinuous dynamical system; Filippov solution; Global asymptotic stability

Indexed keywords

CONVERGENCE IN FINITE TIME; DIFFERENTIAL INCLUSION; DISCONTINUOUS DYNAMICAL SYSTEM; FILIPPOV SOLUTION; GLOBAL ASYMPTOTIC STABILITY;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; CHEMICAL ACTIVATION; DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; NEURAL NETWORKS; SET THEORY;

SYSTEM STABILITY;

ARTICLE; ARTIFICIAL NEURAL NETWORK; MATHEMATICAL MODEL; PRIORITY JOURNAL; SIMULATION;

ANIMALS; COMPUTER SIMULATION; HUMANS; INFORMATION STORAGE AND RETRIEVAL; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); NEURONS; NONLINEAR DYNAMICS; TIME FACTORS;

EID: 69449098824     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2009.04.004     Document Type: Article

References (23)

1. Arik S., and Tavsanoglu V. On the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Circuits Syst. 47 (2000) 571-574
2. Aubin J.P. Viability theory (1991), Birhauser, Boston
3. Aubin J.P., and Celliana A. Differential inclusions (1984), Springer-Verlag, Berlin, Germany
4. Aubin J.P., and Frankowska H. Set-valued analysis (1990), Birkauser, Boston, MA
5. Baciotti, A., Conti, R., & Marcellini, P. (2000). Discontinuous ordinary differential equations and stabilization. Universita di Firenze
6. Chen T., and Amari S. Stability of asymmetric Hopfield networks. IEEE Trans. Neural Netw. 12 1 (2001) 159-163
7. Clarke F.H. Optimization and nonsmooth analysis (1983), Wiley, New York
8. Cohen M.A., and Grossberg S. Absolute stability and global pattern formation and parallel storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13 (1983) 815-826
9. Filippov A.F. Differential equations with discontinuous right-hand side. Mathematics and its applications (Soviet series) (1988), Kluwer Academic, Boston, MA
10. Forti M. On global asymptotic stability of a class nonlinear systems arising in neural network theory. J. Differential Equations 113 (1994) 246-264
11. Forti M., Grazzini M., and Nistri P. Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipchitz activations. Physica D 214 (2006) 88-89
12. Forti M., and Nistri P. Global convergence of neural networks with discontinuous neuron activations. IEEE Trans. Circuits Syst. 50 11 (2003) 1421-1435
13. Hirsch M. Convergent activation dynamics in continuous time networks. Neural Netw. 2 (1989) 331-349
14. Hopfield J.J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. 81 (1984) 3088-3092
15. Horn R.A., and Johnson C.R. Matrix analysis (1985), Cambridge University Press, New York
16. Kaszkurewiez E., and Bhaya A. On a class of globally stable neural circuits. IEEE Trans. Circuits Syst. 41 (1994) 171-174
17. Li J.H., Michel A.N., and Porod W. Analysis and synthesis of a class of neural networks: Variable structure systems with infinite gain. IEEE Trans. Circuits Syst. 36 (1989) 713-731
18. Liang X., and Wang J. An additive diagonal stability condition for absolute stability of a general class of neural networks. IEEE Trans. Circuits Syst. 48 (2001) 1308-1317
19. Lu W.L., and Chen T.P. Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions. Neural Netw. 18 (2005) 231-242
20. Miller R.K., and Michel A.N. Ordinary differential equations (1982), Academic Press, Orlando, FL
21. Paden B.E., and Sastry S.S. Calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulator. IEEE Trans. Circuits and Syst. 34 (1987) 73-82
22. Tank D.W., and Hopfield J.J. Simple neural optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans. Circuits Syst. 33 (1986) 533-541
23. Utkin V.I. Sliding modes and their applications in variable structure systems (1978), MIR Publishers, Moscow