  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.
