Extended Chaos Theory and Multiparticle Production
  First, using the method of the soliton-solution, the fermion probability density equation, which corresponds to the Dirac equation, is derived. Next, we extend the chaos theory, in which the period bifurcation is equivalent to the particle production. Then this extended chaos theory can be used for description of the multiparticle production and the extensive air showers at high energy. Let the parameter takes a suitable value, the quantitative results will be obtained, and an approximate formula will be derived. Many properties of the multiparticle production and of the chaos theory are universal. 
Yi-Fang Chang