Stability of a class of nonreciprocal cellular neural networks

Cellular neural networks with an appropriate choice of templates can solve, among other things, local and global pattern recognition problems. The complete stability of these networks has been proved earlier for the symmetric (reciprocal) cases where the feedback values between the different cells within a neighborhood are the same in both directions. It is shown that at least for some interesting classes of templates, this symmetry (reciprocity) condition is in general not necessary for complete stability. Moreover, the conditions discussed are robust in the sense that they require neither precise template-value relations nor a closeness to some prescribed values. On the other hand, examples are shown of cases where violating some basic conditions would give rise to oscillations.<>