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The stability of a system of neural networks connected to a ring has been studied extensively throughout recent years. Our main contribution within this work states that the stability region in the parameter space of a discrete-time model can be extended by breaking such a ring provided that there is a sufficiently large number of networks. Also, it has been shown that for a small ring, paradoxical values may appear within its parameter space for which such a ring is stable; meanwhile, corresponding linear configuration is unstable.

On the stability of the Cartesian product of a neural ring and an arbitrary neural network