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A path‐following method for finding multiple equilibrium points in cellular neural networks
Author(s) -
Vandenberghe Lieven,
Vandewalle Joos
Publication year - 1992
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490200507
Subject(s) - equilibrium point , artificial neural network , piecewise linear function , computation , path (computing) , mathematics , cellular neural network , relation (database) , mathematical optimization , computer science , character (mathematics) , matrix (chemical analysis) , interconnection , piecewise , algorithm , mathematical analysis , artificial intelligence , computer network , materials science , geometry , database , composite material , programming language , differential equation
Owing to the piecewise linear character of the non‐linearities, the computation of equilibrium points in a cellular neural network could be accomplished in a trivial way by solving 3 n linear systems (where n is the number of neurons). This is clearly infeasible even for moderate n and it is the purpose of this paper to present a more efficient path‐following method for computing equilibrium points. the method is guaranteed to find at least one solution. the possibility of finding all solutions is also investigated and this leads to new theoretical insight to the relation between the properties of the interconnection matrix and the number of equilibrium points.