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Global dynamic behaviour of a three‐cell connected component detector cnn
Author(s) -
Civalleri Pier Paolo,
Gilli Marco
Publication year - 1995
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.4490230204
Subject(s) - planar , limit (mathematics) , mathematics , saddle , limit cycle , graph , plane (geometry) , planar graph , component (thermodynamics) , saddle point , attraction , connected component , combinatorics , mathematical analysis , topology (electrical circuits) , pure mathematics , control theory (sociology) , physics , computer science , geometry , mathematical optimization , artificial intelligence , control (management) , quantum mechanics , linguistics , computer graphics (images) , philosophy
The global dynamic behaviour of a three‐cell connected component detector CNN described by the template [‐ s, p, s ] is addressed. In the case p ‐1 > s > O the structure of the domains of attraction of the stable equilibria and the stable manifolds of the saddle points is represented by means of a suitable planar graph. In the case s > p ‐ 1 > O it is shown that five stable and two unstable limit cycles occur. It is proved that one of the stable cycles lies entirely on the plane x 1 = ‐ x 3 whereas the others have the property that the second cell works only in the linear part of the output characteristic. Moreover, the domains of attraction of the stable cycles are found to be separated by the stable manifolds of the unstable equilibria (still existing for s > p ‐ 1 > O ) and of the above two unstable limit cycles.