Stochastic stability analysis of competitive neural networks with different time-scales

Neurocomputing

Volumn 118, Issue , 2013, Pages 115-118

  Meyer Bäse, Anke ^a   Botella, Guillermo ^b   Rybarska Rusinek, Liliana ^c  

^a FLORIDA STATE UNIVERSITY   (United States)

^b FAMU FSU COLLEGE OF ENGINEERING   (United States)

^c Rzeszow University of Technology Rzeszow   (Poland)

Author keywords

Competitive neural networks; Long and short term memory; Singularly perturbed system; Stochastic stability

Indexed keywords

COMPETITIVE NEURAL NETWORK; MEAN SQUARE STABILITY; REDUCED ORDER MODELS; SHORT TERM MEMORY; SINGULARLY PERTURBED; SINGULARLY PERTURBED SYSTEMS; STOCHASTIC NONLINEAR SYSTEMS; STOCHASTIC STABILITY;

LYAPUNOV FUNCTIONS; PERTURBATION TECHNIQUES; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; CELL ACTIVATION; LEARNING; LONG TERM MEMORY; MATHEMATICAL ANALYSIS; MOLECULAR DYNAMICS; MOLECULAR STABILITY; NERVE CELL NETWORK; NONLINEAR SYSTEM; PRIORITY JOURNAL; PROCESS MODEL; SHORT TERM MEMORY; STOCHASTIC MODEL; SYNAPTIC TRANSMISSION; VALIDATION PROCESS;

EID: 84881221314     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2013.02.020     Document Type: Article

References (18)

1. Meyer-Baese A., Pilyugin S.S., Chen Y. Global exponential stability of competitive neural networks with different time scales. Trans. Neural Networks 2003, 14:716-719.
2. Mou S., Gao H., Lam J., Qiang W. A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay. Trans. Neural Networks 2008, 19:532-535.
3. Wan L., Sun J. Mean square stability of stochastic delayed Hopfield neural networks. Phys. Lett. A 2005, 343:306-318.
4. Kim J.-H. Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty. IEEE Trans. Autom. Control 2001, 46:789-792.
5. Feng W., Yang S.X., Fu W., Wu H. Robust stability analysis of uncertain stochastic neural networks with interval time-varying delay. Chaos Solitons Fractals 2009, 41:414-424.
6. Zhao Y., Zhang L., Shen S., Gao H. Robust stability criterion for discrete-time uncertain Markovian jumping neural networks with defective statistics of modes transitions. IEEE Trans. Proc. - Int. Conf. Neural Networks 2011, 22:164-170.
7. Gu H., Jiang H., Teng Z. Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays. J. Franklin Inst. 2010, 347:719-731.
8. Meyer-Bäse A., Roberts R., Yu H. Robust stability analysis of competitive neural networks with different time-scales under perturbations. Neurocomputing 2007, 71:417-420.
9. Lu H., He Z. Global exponential stability of delayed competitive neural networks with different time scales. Neural Networks 2005, 18:243-250.
10. Meyer-Bäse A., Roberts R., Thümmler V. Local uniform stability of competitive neural networks with different time-scales under vanishing perturbations. Neurocomputing 2010, 73:770-775.
11. Lou X., Cui B. Synchronization of competitive neural networks with different time scales. Physica A. Stat. Mech. Appl. 2007, 380:563-576.
12. Meyer-Bäse A., Koshkouei A.J., Emmett M.R., Goodall D.P. Global stability analysis and robust design of multi-time-scale biological networks under parametric uncertainties. Neural Networks 2009, 22:658-663.
13. Y. Kao, Q. Ming, Global robust stability of competitive neural networks with continuously distributed delays and different time scales, in: Proceedings of the 17th International Conference on Artificial Neural Networks, ICANN'07, Springer-Verlag, Berlin, Heidelberg, 2007, pp. 569-578.
14. Gu H. Adaptive synchronization for competitive neural networks with different time scales and stochastic perturbation. Neurocomputing 2009, 73:350-356.
15. L. Rybarska-Rusinek, L. Socha, String stability of singularly perturbed stochastic systems with Gaussian excitations, in: American Control Conference, 2003. Proceedings of the 2003, vol. 5, 2003, pp. 4432-4437.
16. Stam C., Hillebrand A., Wang H., Mieghem P.V. Emergence of modular structure in a large-scale brain network with interactions between dynamics and connectivity. Front. Neurosci. 2010, 4:1-13.
17. Corless M., Glielmo L. On exponential stability of singularly perturbed systems. SIAM J. Control Optim. 1998, 30:375-405.
18. Hasminskii R.Z. Stochastic Stability of Differential Equations 1980, Kluwer Academic Publication.