  This paper is the forth part of our series of work, is devoted to the
analysis on the multiscales and cascade aspects of the statistical theory of
isotropic turbulence based on the new Sedov-type solution. In this paper, we
use the explicit map method to analyse the nonlinear dynamical behaviour for
cascade in isotorpic turbulence. This deductive scale analysis is shown to
provide the first visual evidence of the celebrated Richardson cascade, and
reveals in partcular its multiscale character. The results also indicate that
the energy cascading process has remarkable similarities with the
determinisitic construction rules of the logistic map. Cascade of
period-doubling bifurcations have been seen in this isotropic turbuent systems
that exhibit chaotic behaviour. The 'cascade' appears as an infinite sequence
of period-doubling bifurcations.
