{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T06:45:57Z","timestamp":1761806757225,"version":"3.30.1"},"reference-count":66,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[1999,3,1]],"date-time":"1999-03-01T00:00:00Z","timestamp":920246400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Networks"],"published-print":{"date-parts":[[1999,3]]},"DOI":"10.1016\/s0893-6080(98)00118-x","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T23:57:31Z","timestamp":1027641451000},"page":"259-271","source":"Crossref","is-referenced-by-count":8,"title":["Analysis and optimal design of continuous neural networks with applications to associative memory"],"prefix":"10.1016","volume":"12","author":[{"given":"Miao","family":"Zhenjiang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Baozong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0893-6080(98)00118-X_BIB1","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1109\/T-C.1972.223477","article-title":"Learning patterns and pattern sequences by self-organizing nets of threshold elements","volume":"21","author":"Amari","year":"1972","journal-title":"IEEE Trans. Computers"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB2","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/BF00365229","article-title":"Neural theory of association and concept formation","volume":"26","author":"Amari","year":"1977","journal-title":"Biol. Cybern."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB3","unstructured":"Amari, S. (1987). On mathematical methods in the theory of neural networks. In Proceedings of IEEE International Conference on Neural Networks (Vol. III. pp. 3\u201310), San Diego, CA."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB4","doi-asserted-by":"crossref","unstructured":"Amari, S. (1988). Statistical neurodynamics of various versions of correlation associative memory. In Proceedings of IEEE International Conference on Neural Networks (Vol. I, pp. 633\u2013640), San Diego, CA.","DOI":"10.1109\/ICNN.1988.23900"},{"issue":"5","key":"10.1016\/S0893-6080(98)00118-X_BIB5","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1109\/72.623200","article-title":"Asymptotic statistical theory of overtraining and cross-validation","volume":"8","author":"Amari","year":"1997","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB6","unstructured":"Bertsekas, D.P. (1995). Nonlinear programming (pp. 253\u2013415). Belmont, MA: Athena Scientific."},{"issue":"6","key":"10.1016\/S0893-6080(98)00118-X_BIB7","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1109\/72.548184","article-title":"A note on stability of analog neural networks with time delays","volume":"7","author":"Cao","year":"1996","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB8","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1109\/2.33","article-title":"The ART of adaptive pattern recognition by a self-organizing neural network","volume":"March","author":"Carpenter","year":"1988","journal-title":"Computer"},{"issue":"10","key":"10.1016\/S0893-6080(98)00118-X_BIB9","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1109\/31.7601","article-title":"Cellular neural networks: applications","volume":"35","author":"Chua","year":"1988","journal-title":"IEEE Trans. Circuits and Systems"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB10","unstructured":"Cohen, M.A. (1987). Sustained oscillations in symmetric cooperative-competitive neural networks. In Proc. of IEEE International Conference on Neural Networks (Vol. II, pp. 127\u2013129), San Diego, CA."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB11","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1109\/TSMC.1983.6313075","article-title":"Absolute stability of global pattern formation and parallel memory storage by competitive neural networks","volume":"13","author":"Cohen","year":"1983","journal-title":"IEEE Trans. Systems, Man, and Cybernetics"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB12","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1080\/08839518908949917","article-title":"Replacing symbolic rule system with PDP NetworksNetzsprech: a German example","volume":"3","author":"Dorffner","year":"1989","journal-title":"Applied Artificial Intelligence"},{"issue":"4","key":"10.1016\/S0893-6080(98)00118-X_BIB13","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1109\/72.508941","article-title":"Stability analysis of dynamical neural networks","volume":"7","author":"Fang","year":"1996","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB14","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1109\/31.55063","article-title":"A synthesis procedure for Hopfield's continuous-time associative memory","volume":"37","author":"Farrell","year":"1990","journal-title":"IEEE Trans. CAS"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB15","unstructured":"Franklin, J.N. (1968). Matrix theory (pp. 105, 141\u2013146, 161). Englewood Cliffs, NJ: Prentice-Hall."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB16","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1109\/2.32","article-title":"A neural network for visual pattern recognition","volume":"March","author":"Fukushima","year":"1988","journal-title":"Computer"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB17","unstructured":"Gibson, J.E. (1963). Nonlinear automatic control. New York: McGraw-Hill."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB18","unstructured":"Golub, G.H., & Loan, C.F.V. (1996). Matrix computations (3rd ed., pp. 140, 310). Baltimore, MD: The Johns Hopkins University Press."},{"issue":"2","key":"10.1016\/S0893-6080(98)00118-X_BIB19","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1109\/72.557672","article-title":"Convergence under dynamical thresholds with delays","volume":"8","author":"Gopalsamy","year":"1997","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB20","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/0022-2496(69)90003-0","article-title":"Embedding field: a theory of learning with physiological implications","volume":"6","author":"Grossberg","year":"1969","journal-title":"J. Math. Psych."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB21","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF01007484","article-title":"On learning and energy\u2013entropy dependence in recurrent and nonrecurrent signed networks","volume":"1","author":"Grossberg","year":"1969","journal-title":"J. Stat. Phys."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB22","doi-asserted-by":"crossref","unstructured":"Grossberg, S. (1982). Studies of mind and brain: neural principles of learning, perception, development, cognition and motor control. Boston, MA: Reidel.","DOI":"10.1007\/978-94-009-7758-7"},{"issue":"1","key":"10.1016\/S0893-6080(98)00118-X_BIB23","first-page":"80","article-title":"On the stability, storage capacity, and design of nonlinear continuous neural networks","volume":"18","author":"Guez","year":"1988","journal-title":"IEEE Trans. SMC"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB24","unstructured":"Hinton, G.E., & Anderson, J.A. (1981). Parallel models of an associative memory. Hillsdale, NJ: Erlbaum."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB25","unstructured":"Hirsch, M.W. (1987). Convergence in neural nets. In Proceedings of IEEE International Conference on Neural Networks (Vol. II), San Diego, CA."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB26","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/0893-6080(89)90018-X","article-title":"Convergent activation dynamics in continuous time networks","volume":"2","author":"Hirsch","year":"1989","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB27","doi-asserted-by":"crossref","first-page":"3088","DOI":"10.1073\/pnas.81.10.3088","article-title":"Neurons with graded response have collective computational properties like those of two-state neurons","volume":"81","author":"Hopfield","year":"1984","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB28","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1109\/TAC.1961.1105195","article-title":"A modified Lyapunov method for nonlinear stability analysis","volume":"AC6","author":"Ingwerson","year":"1961","journal-title":"IRE Trans. Automatic Control"},{"issue":"4","key":"10.1016\/S0893-6080(98)00118-X_BIB29","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1109\/72.508944","article-title":"Globally asymptotical stability of discrete-time analog neural networks","volume":"7","author":"Jin","year":"1996","journal-title":"IEEE Trans. Neural Networks"},{"issue":"6","key":"10.1016\/S0893-6080(98)00118-X_BIB30","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1109\/29.56063","article-title":"Classification of invariant image representations using a neural network","volume":"18","author":"Khotanzad","year":"1990","journal-title":"IEEE Trans. ASSP"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB31","unstructured":"Kohonen, T. (1984). Self-organization and associative memory. Berlin: Springer."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB32","doi-asserted-by":"crossref","first-page":"4947","DOI":"10.1364\/AO.26.004947","article-title":"Adaptive bidirectional associative memories","volume":"26","author":"Kosko","year":"1987","journal-title":"Applied Optics"},{"issue":"1","key":"10.1016\/S0893-6080(98)00118-X_BIB33","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1109\/21.87054","article-title":"Bidirectional associative memories","volume":"18","author":"Kosko","year":"1988","journal-title":"IEEE Trans. System, Man, and Cybernetics"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB34","first-page":"735","article-title":"On the global stability of a system of nonlinear differential equations (in Russian)","volume":"18","author":"Krasovskii","year":"1954","journal-title":"Applied Mathematics and Mechanics (Prikladnaja Matematika i Mekanika)"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB35","unstructured":"Krasovskii, N.N. (1963). Stability of motion. Stanford, CA: Stanford University Press."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB36","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1109\/31.1844","article-title":"Qualitative analysis and synthesis of a class of neural networks","volume":"35","author":"Lin","year":"1988","journal-title":"IEEE Trans. CAS"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB37","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1109\/31.41297","article-title":"Analysis and synthesis of a class of neural networks: linear systems operating on a closed hypercube","volume":"36","author":"Lin","year":"1989","journal-title":"IEEE Trans. CAS"},{"issue":"1","key":"10.1016\/S0893-6080(98)00118-X_BIB38","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/72.80293","article-title":"A hierarchical multiple-view approach to three dimensional object recognition","volume":"2","author":"Lin","year":"1991","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB39","unstructured":"Luenberger, D.G. (1984). Linear and nonlinear programming (2nd ed). Reading, MA: Addison-Wesley."},{"issue":"5","key":"10.1016\/S0893-6080(98)00118-X_BIB40","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/0031-3203(89)90019-8","article-title":"Edge detection by associative mapping","volume":"22","author":"Meer","year":"1989","journal-title":"Pattern Recognition"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB41","doi-asserted-by":"crossref","unstructured":"Miao, Z.-J., & Yuan, B.-Z. (1993a). An extended BAM neural network model. In Proceedings of IJCNN (Vol. 3, pp. 2682\u20132685), Nagoya, Japan.","DOI":"10.1109\/IJCNN.1993.714276"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB42","unstructured":"Miao, Z.-J., & Yuan, B.-Z. (1993b). Loop neural network model for associative memory. In Proceedings of IEEE TENCON'93 (Vol. 2, pp. 758\u2013762), Beijing, China."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB43","unstructured":"Miao, Z.-J., & Yuan, B.-Z. (1993c). A new analytical method for AM neural networks and its application to pattern recognition. In Proceedings of 1993 IEEE International Conference on Neural Networks, San Francisco, CA."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB44","unstructured":"Miao, Z.-J., & Yuan, B.-Z. (1993d). A NN image understanding system for maps and animals recognition. In Proceedings of IEEE TENCON'93 (Vol. 2, pp. 902\u2013905), Beijing, China."},{"issue":"6","key":"10.1016\/S0893-6080(98)00118-X_BIB45","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/0952-1976(94)90064-7","article-title":"MIPAS: a neural-network-based multimedia information processing and analyzing system","volume":"7","author":"Miao","year":"1994","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB46","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1109\/31.20200","article-title":"Qualitative analysis of neural networks","volume":"36","author":"Michel","year":"1989","journal-title":"IEEE Trans. CAS"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB47","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1109\/31.62410","article-title":"Analysis and synthesis techniques for Hopfield type synchronous discrete time neural networks with application to associative memory","volume":"37","author":"Michel","year":"1990","journal-title":"IEEE Trans. CAS"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB48","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/37.55118","article-title":"Associative memories via artificial neural networks","volume":"April","author":"Michel","year":"1990","journal-title":"IEEE Control Systems Magazine"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB49","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/72.80289","article-title":"Analysis and synthesis of a class of discrete-time neural networks described on hypercubes","volume":"2","author":"Michel","year":"1991","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB50","unstructured":"Ogata, K. (1970). Modern control engineering (pp. 735\u2013736). Englewood Cliffs, NJ: Prentice-Hall."},{"issue":"3","key":"10.1016\/S0893-6080(98)00118-X_BIB51","first-page":"323","article-title":"The determination of the generalized diagonally dominant matrix and its applications","volume":"6A","author":"Pang","year":"1985","journal-title":"Chinese Annals of Mathematics"},{"issue":"8","key":"10.1016\/S0893-6080(98)00118-X_BIB52","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1109\/34.57670","article-title":"Selective and focused invariant recognition using distributed associative memories (DAM)","volume":"12","author":"Polzleitner","year":"1990","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB53","unstructured":"Renardy, M., & Rogers, R.C. (1993). An introduction to partial differential equations (pp. 5\u20137). New York: Springer."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB54","unstructured":"Schultz, D.G. (1965). The generation of Lyapunov functions. In C.T. Leondes (Ed.), Advances in control systems (pp. 1\u201364). New York: Academic Press."},{"issue":"II","key":"10.1016\/S0893-6080(98)00118-X_BIB55","first-page":"203","article-title":"The variable gradient method for generating Lyapunov functions","volume":"81","author":"Schultz","year":"1962","journal-title":"IEEE Trans."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB56","doi-asserted-by":"crossref","unstructured":"Schurmann, B. (1989a). Generalized adaptive bidirectional associative memory. In Proceedings of IEEE International Conference on Neural Networks (Vol. I, pp. 91\u201397), Washington, DC.","DOI":"10.1109\/IJCNN.1989.118564"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB57","doi-asserted-by":"crossref","first-page":"2681","DOI":"10.1103\/PhysRevA.40.2681","article-title":"Stability and adaptation in artificial intelligence neural systems","volume":"A40","author":"Schurmann","year":"1989","journal-title":"Phys. Rev."},{"issue":"2","key":"10.1016\/S0893-6080(98)00118-X_BIB58","first-page":"143","article-title":"Some necessary and sufficient conditions for generalized diagonal dominant matrix","volume":"7","author":"Sun","year":"1987","journal-title":"Journal of Mathematics"},{"issue":"3","key":"10.1016\/S0893-6080(98)00118-X_BIB59","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/72.501721","article-title":"An approach to stability criteria of neural-network control system","volume":"7","author":"Tanaka","year":"1996","journal-title":"IEEE Trans. Neural Networks"},{"issue":"4","key":"10.1016\/S0893-6080(98)00118-X_BIB60","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/0893-6080(95)00121-2","article-title":"Stability of a class of directionally sensitive asymmetric nonlinear neural networks","volume":"9","author":"Tonkin","year":"1996","journal-title":"Neural Networks"},{"issue":"6","key":"10.1016\/S0893-6080(98)00118-X_BIB61","first-page":"659","article-title":"Distribution of the characteristic roots of matrix and their applications to the stability theory","volume":"8A","author":"Tu","year":"1987","journal-title":"Chinese Annals of Mathematics"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB62","unstructured":"Vincent, T.L., & Grantham, M.J. (1997). Nonlinear and optimal control systems (pp. 221\u2013239). New York: Wiley."},{"key":"10.1016\/S0893-6080(98)00118-X_BIB63","unstructured":"Yoshizawa, S., Worita, M., Doya, K., & Amari, S. (1991). Analysis of dynamics of an associative neural network with non-monotonic output function. In T. Kohonen et al. (Ed.), Artificial neural networks (pp. 255\u2013260). Amsterdam: North-Holland\/Elsevier Science."},{"issue":"2","key":"10.1016\/S0893-6080(98)00118-X_BIB64","first-page":"309","article-title":"Distribution of the eigenvalues for conjugate generalized diagonally dominant matrices","volume":"9","author":"You","year":"1989","journal-title":"Journal of Mathematical Research and Exposition"},{"key":"10.1016\/S0893-6080(98)00118-X_BIB65","unstructured":"Zhen, G. (1985). The applications of Lyapunov direct method in automatic control. Shanghai: Shanghai Science Publishing House."},{"issue":"7","key":"10.1016\/S0893-6080(98)00118-X_BIB66","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1109\/29.1641","article-title":"Image restoration using neural network","volume":"36","author":"Zhou","year":"1988","journal-title":"IEEE Trans. Acoustic, Speech, and Signal Processing"}],"container-title":["Neural Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S089360809800118X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S089360809800118X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T01:25:15Z","timestamp":1733448315000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S089360809800118X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,3]]},"references-count":66,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1999,3]]}},"alternative-id":["S089360809800118X"],"URL":"https:\/\/doi.org\/10.1016\/s0893-6080(98)00118-x","relation":{},"ISSN":["0893-6080"],"issn-type":[{"type":"print","value":"0893-6080"}],"subject":[],"published":{"date-parts":[[1999,3]]}}}