Multistable learning dynamics in second-order neural networks with time-varying delays

References

• Abu-Mostafa , Y. and Jacques , J. 1985 . Information capacity of the Hopfield model . IEEE Trans. Inform. Theory , 31 : 461 – 464 .
   Web of Science ®Google Scholar
• Amari , S. 1991 . Mathematical theory of neural learning . New Gener. Comput. , 8 : 281 – 294 .
   Google Scholar
• Cao , J. D. , Feng , G. and Wang , Y. 2008 . Multistability and multiperiodicity of delayed Cohen-Grossberg neural networks with a general class of activation functions . Physica D , 237 ( 13 ) : 1734 – 1749 .
   Google Scholar
• Cao , J. , Liang , J. and Lam , J. 2004 . Exponential stability of high-order bidirectional associative memory neural networks with time delays . Physica D , 199 ( 3 ) : 425 – 436 .
   Google Scholar
• Carpenter , G. A. and Grossberg , S. 1987 . A massively parallel architecture for a self-organizing neural pattern recognition machine . Comput. Vis. Graph. Image Process. , 37 : 54 – 115 .
   Google Scholar
• Cheng , C. , Lin , K. and Shih , C. 2007 . Multistability and convergence in delayed neural networks . Physica D , 225 : 61 – 74 .
   Google Scholar
• Cohen , M. A. and Grossberg , S. 1983 . Absolute stability of global pattern formation and parallel memory storage by competitive neural networks . IEEE Trans. Syst. Man Cybern. , 13 : 815 – 826 .
   Web of Science ®Google Scholar
• Dembo , A. , Farotimi , O. and Kailath , T. 1991 . High-order absolutely stable neural networks . IEEE Trans. Circuits Syst. , 38 ( 1 ) : 57 – 65 .
   Google Scholar
• Feng , C. H. and Plamondon , R. 2001 . On the stability analysis of delayed neural networks systems . Neural Netw. , 14 ( 9 ) : 1181 – 1188 .
   PubMed Web of Science ®Google Scholar
• Feng , C. H. and Plamondon , R. 2003 . Stability analysis of bidirectional associative memory networks with time delays . IEEE Trans. Neural Netw. , 14 ( 6 ) : 1560 – 1565 .
   PubMedGoogle Scholar
• Gopalsamy , K. 2007 . Learning dynamics in second order networks . Nonlin. Anal., Real World Appl. , 8 ( 2 ) : 688 – 698 .
   Google Scholar
• Gopalsamy , K. 2006 . Second order neurons and learning in Cohen-Grossberg networks . Int. J. Neural Syst. , 16 ( 3 ) : 179 – 189 .
   PubMedGoogle Scholar
• Huang , G. and Cao , J. D. 2008 . Multistability in bidirectional associative memory neural networks . Phys. Lett. A , 372 ( 16 ) : 2842 – 2854 .
   Google Scholar
• Huang , Z. K. , Mohamad , S. , Wang , X. H. and Feng , C. H. 2009 . Convergence analysis of general neural networks under almost periodic stimuli . Int. J. Circuit Theory Appl. , 37 : 723 – 750 .
   Google Scholar
• Huang , Z. K. , Mohamad , S. and Bin , H. 2009 . Multistability of HNNs with almost periodic stimuli and continuously distributed delays . Int. J. Syst. Sci. , 40 ( 6 ) : 615 – 625 .
   Web of Science ®Google Scholar
• Huang , Z. K. , Song , Q. and Feng , C. 2010 . Multistability in networks with self-excitation and high-order synaptic connectivity . IEEE Trans. Circuits Syst. I, Reg. Papers , 57 ( 8 ) : 2144 – 2155 .
   Google Scholar
• Huang , Z. K. and Xia , Y. H. 2007 . Exponential p-stability of second order Cohen-Grossberg neural networks with transmission delays and learning behavior . Simulation Modelling Pract. Theory , 15 : 622 – 634 .
   Google Scholar
• Kosmatopoulos , E. B. and Christodoulou , M. A. 1995 . Structural properties of gradient recurrent high-order neural networks . IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. , 42 ( 9 ) : 592 – 603 .
   Google Scholar
• Liu , X. , Teo , K. L. and Xu , B. 2005 . Exponential stability of impulsive high-order Hopfield type neural networks with time varying delays . IEEE Trans. Neural Netw. , 16 : 1329 – 1339 .
   PubMed Web of Science ®Google Scholar
• Lou , X. and Cui , B. 2007 . Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays . J. Math. Anal. Appl. , 330 : 144 – 158 .
   Web of Science ®Google Scholar
• Lu , H. and Amari , S. 2006 . Global exponential stability of multitime scale competitive neural networks with nonsmooth functions . IEEE Trans. Neural Netw. , 17 ( 5 ) : 1152 – 1164 .
   PubMedGoogle Scholar
• Meyer-Baese , A. , Pilyugin , S. S. and Chen , Y. 2003 . Global exponential stability of competitive neural networks with different time scales . IEEE Trans. Neural Netw. , 14 : 716 – 719 .
   PubMedGoogle Scholar
• Nie , X. and Cao , J. D. 2009 . Multistability of competitive neural networks wtih time-varying and distributed delays . Nonlinear Anal., Real World Appl. , 10 ( 2 ) : 928 – 942 .
   Google Scholar
• Paretto , P. and Niez , J. J. 1986 . Long term memory storage capacity of multiconnected neural networks . Biol. Cybern. , 54 : 53 – 63 .
   PubMed Web of Science ®Google Scholar
• Psaltis , D. , Park , C. H. and Hong , J. 1988 . Higher-order associative memories and their optical implementations . Neural Netw. , 1 ( 2 ) : 149 – 163 .
   Google Scholar
• Ren , F. and Cao , J. 2007 . Periodic oscillation of higher-order BAM neural networks with periodic coefficients and delays . Nonlinearity , 20 ( 3 ) : 605 – 629 .
   Google Scholar
• Shih , C. and Tseng , J. 2008 . Convergent dynamics for multistable delayed neural networks . Nonlinearity , 21 ( 10 ) : 2361 – 2389 .
   Google Scholar
• Simpson , P. K. 1990 . Higher-ordered and intraconnected bidirectional associative memories . IEEE Trans. Syst. Man Cybern. , 20 : 637 – 653 .
   Web of Science ®Google Scholar
• Wang , L. and Zou , X. H. 2004 . Capacity of stable periodic solutions in discrete-time bidirectional associative memory neural networks . IEEE Trans. Circuits Syst. II, Exp. Briefs , 51 ( 6 ) : 315 – 319 .
   Google Scholar
• Xia , Y. H. , Yang , Z. and Han , M. 2009 . Lag synchronization of chaotic delayed Yang-Yang type fuzzy neural networks with noise perturbation based on adaptive control and parameter identification . IEEE Trans. Neural Netw. , 20 ( 7 ) : 1165 – 1180 .
   PubMedGoogle Scholar
• Xu , B. , Liu , X. and Liao , X. 2006 . Global exponential stability of high-order Hopfield type neural networks . Appl. Math. Comput. , 174 : 98 – 116 .
   Web of Science ®Google Scholar
• Zeng , Z. G. and Wang , J. 2006 . Multiperiodicity of discrete-time delayed neural networks evoked by periodic external inputs . IEEE Trans. Neural Netw. , 17 ( 5 ) : 1141 – 1151 .
   PubMedGoogle Scholar
• Zhang , B. , Xu , S. , Li , Y. and Chu , Y. 2007 . On global exponential stability of high-order neural networks with time-varying delays . Phys. Lett. A , 366 : 69 – 78 .
   Web of Science ®Google Scholar