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The permutation binary neural networks are characterized by globalpermutation connections and local binary connections. Although the parameterspace is not large, the networks exhibit various binary periodic orbits. Sinceanalysis of all the periodic orbits is not easy, we focus on globally stablebinary periodic orbits such that almost all initial points fall into theorbits. For efficient analysis, we define the standard permutation connectionthat represents multiple equivalent permutation connections. Applying the bruteforce attack to 7-dimensional networks, we present the main result: a list ofstandard permutation connections for all the globally stable periodic orbits.These results will be developed into detailed analysis of the networks and itsengineering applications.

A variety of globally stable periodic orbits in permutation binary neural networks