  This paper presents a permutation binary neural network characterized by
local binary connection, global permutation connection, and the signum
activation function. The dynamics is described by a difference equation of
binary state variables. Depending on the connection, the network generates
various periodic orbits of binary vectors. The binary/permutation connection
brings benefits to precise analysis and to FPGA based hardware implementation.
In order to consider the periodic orbits, we introduce three tools: a
composition return map for visualization of the dynamics, two feature
quantities for classification of periodic orbits, and an FPGA based hardware
prototype for engineering applications. Using the tools, we have analyzed all
the 6-dimensional networks. Typical periodic orbits are confirmed
experimentally.
