Pitchfork bifurcation of a class of discrete dynamical systems

A class of discrete dynamical systems is introduced to unify various dynamical systems that appeared in the study of phase transition phenomenon of Ising model on the Cayley tree. We give an alternative method to study the stable fixed points of these dynamical systems. The regions of non-uniqueness of stable fixed point and single stable fixed point are immediately obtained. All the previous results could be derived using this criterion.