  This paper studies a permutation binary neural network characterized by local
binary connections, global permutation connections, and the signum activation
function. Depending on the permutation connections, the network can generate
various periodic orbits of binary vectors. Especially, we focus on globally
stable periodic orbits such that almost all initial points fall into the
orbits. In order to explore the periodic orbits, we present a simple
evolutionary algorithm. Applying the algorithm to typical examples of PBNNs,
existence of a variety of periodic orbits is clarified. Presenting an FPGA
based hardware prototype, typical periodic orbits are confirmed experimentally.
The hardware will be developed into various engineering applications such that
stable control signals of switching circuits and stable approximation signals
of time-series.
