Asymptotic solutions of a class of matrix differential equations arising in neutral network modelling
作者:
ERKKI OJA,
期刊:
International Journal of Systems Science
(Taylor Available online 1977)
卷期:
Volume 8,
issue 10
页码: 1145-1161
ISSN:0020-7721
年代: 1977
DOI:10.1080/00207727708942110
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The following matrix differential equation initiated by research of dynamical network models is studied: φ=-P(φ t)a(t)a(t)TP(φT,t), where a is a vector-valued function of time t and P is a matrix-valued function of the solution matrix and time. A set of assumptions is given under which the solution, starting from a symmetric positive sotnidofinite initial matrix, tends asymptotically to a positive semidefinito matrix; if the initial matrix is a projection matrix and a(t) hua a special step-like structure, then the solution tends to a projection matrix on a specified subspace. Finally, a generalization of the basic class of equations is studied and an explicit expression is given for the limit matrix under certain conditions.
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