Global dynamic behaviour of a three‐cell connected component detector cnn

The global dynamic behaviour of a three‐cell connected component detector CNN described by the template [‐s, p, s] is addressed. In the casep‐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 cases>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 planex1= ‐x3whereas 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 fors>p‐ 1 > O ) and of the above two unstable limit cycles.