Stability analysis of inertial Cohen-Grossberg-type neural networks with time delays

Neurocomputing

Volumn 117, Issue , 2013, Pages 196-205

  Ke, Yunquan ^a   Miao, Chunfang ^a  

^a SHAOXING UNIVERSITY   (China)

Author keywords

Differential mean value theorem; Exponential stability; Homeomorphism; Inertial Cohen Grossberg type; Lyapunov functional; Neural networks

Indexed keywords

DIFFERENTIAL MEAN VALUE THEOREMS; FIRST ORDER DIFFERENTIAL EQUATION; GLOBAL EXPONENTIAL STABILITY; HOMEOMORPHISM; INERTIAL COHEN-GROSSBERG-TYPE; LYAPUNOV FUNCTIONALS; SUFFICIENT CONDITIONS; VARIABLE SUBSTITUTION;

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; SYSTEM STABILITY; TIME DELAY; TIME VARYING NETWORKS;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; COHEN GROSSBERG NEURAL NETWORK; EXPONENTIAL STABILITY; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; PRIORITY JOURNAL; STATISTICAL CONCEPTS;

EID: 84878931538     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2013.01.026     Document Type: Article

References (26)

1. Cohen M.A., Grossberg S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 1983, 13:815-825.
2. Hiang T. Robust stability of delayed fuzzy Cohen-Grossberg neural networks. Comput. Math. Appl. 2011, 61(8):2247-2250.
3. Hiang T., Li C., Chen G. Stability of Cohen-Grossberg neural networks with unbounded distributed delays. Chaos Solitons Fractals 2007, 34(3):992-996.
4. Gan Q. Exponential synchronization of stochastic Cohen-Grossberg neural networks with mixed time-varying delays and reaction-diffusion via periodically intermittent control. Neural Networks 2012, 31:12-21.
5. Gan Q. Adaptive synchronization of Cohen-Grossberg neural networks with unknown parameters and mixed time-varying delays. Commun. Nonlinear Sci. Numer. Simulation 2012, 17(7):3040-3049.
6. Song Q., Wing Z. Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. Phys. A. Stat. Mech. Appl. 2008, 387(13):3314-3326.
7. Song Q., Zhang J. Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays. Nonlinear Anal. Real World Appl. 2008, 9(2):500-510.
8. Cao J., Liang J. Boundedness and stability for Cohen-Grossberg neural networks with time-varying delays. J. Math. Anal. Appl. 2004, 296:665-685.
9. Cui B., Lou X. Global asymptotic stability of BAM neural networks with distributed delays and reaction-diffusion terms. Chaos Solitons Fractals 2006, 27:1347-1354.
10. Huang T., Chan A., Huang Y., Cao J. Stability of Cohen-Grossberg neural networks with time-varying delays. Neural Networks 2007, 20:868-873.
11. Li K., Song Q. Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms. Neurocomputing 2008, 72:231-240.
12. Li T., Fei S. Stability analysis of Cohen-Grossberg neural networks with time- varying and distributed delays. Neurocomputing 2008, 71:1069-1081.
13. Li Z., Li K. Stability analysis of impulsive Cohen-Grossberg neural networks with distributed delays and reaction-diffusion terms. Appl. Math. Model. 2009, 33:1337-1348.
14. Li C.G., Chen G.R., Liao X.F., Yu J.B. Hopf bifurcation and chaos in a single inertial neuron model with time delay. Eur. Phys. J. B 2004, 41:337-343.
15. Q. Liu, X.F. Liao, G.Y. Wang, Y. Wu, Research for Hopf bifurcation of an inertial two-neuron system with time delay, in: IEEE Proceeding GRC, 2006, pp. 420-423.
16. Q. Liu, X.F. Liao, D.G. Yang, S.T. Guo, The research for Hopf bifurcation in a single inertial neuron model with external forcing, in: IEEE Proceeding GRC, 2007, pp. 528-533.
17. Wheeler Diek W., Schieve W.C. Stability and chaos in an inertial two-neuron system. Physica D 1997, 105:267-284.
18. Babcock K.L., Westervelt R.M. Stability and dynamics of simple electronic neural networks with added inertia. Phys. D. Nonlinear Phenom. 1986, 464-469.
19. Juhong G.E., Jing X.U. Weak resonant double Hopf bifurcations in an inertial four-neuron model with time delay. Int. J. Neural Syst. 2012, 22-63. 10.1142/S0129065712002980.
20. Yo Horikawa, Bifurcation and stabilization of oscillations in ring neural networks with inertia, Physica D 238 (2009) 2409-2418.
21. Liu Q., Liao X., Liu Y., Zhou S., Guo S. Dynamics of an inertial two-neuron system with time delay. Nonlinear Dyn. 2009, 58:573-609.
22. Liu Q., Liao X.F., Guo S.T., Wu Y. Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation. Nonlinear Anal. Real World Appl. 2009, 10:2384-2395.
23. Zhao H.Y., Chen L., Yu X.H. Bifurcation and control of a class of inertial neuron networks. Acta Phys. 2011, 60(7):70202. (1-8).
24. Ke Y.Q., Miao C.F. Stability analysis of BAM neural networks with inertial term and time delay. WSEAS Trans. Syst. 2011, 10(12):425-438.
25. Ke Y.Q., Miao C.F. Stability and existence of periodic solutions in inertial BAM neural networks with time delay. Neural Comput. Appl. 2012, (Online First, 15 July 2012). 10.1007/s00521-012-1037-8.
26. Forti M., Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans. Circuits Syst. I 1995, 42:354-366.