  It has been demonstrated that excitable media with a tree structure performed
better than other network topologies, it is natural to consider neural networks
defined on Cayley trees. The investigation of a symbolic space called
tree-shift of finite type is important when it comes to the discussion of the
equilibrium solutions of neural networks on Cayley trees. Entropy is a
frequently used invariant for measuring the complexity of a system, and
constant entropy for an open set of coupling weights between neurons means that
the specific network is stable. This paper gives a complete characterization
for entropy spectrum of neural networks on Cayley trees and reveals whether the
entropy bifurcates when the coupling weights change.
