  Motivating by the China's five element philosophy (CFEP) we construct a
permuted Volterra quadratic stochastic operator acting on the four dimensional
simplex. This operator (depending on 10 parameters) is considered as an
evolution operator for CFEP. We study the discrete time dynamical system
generated by this operator. Mainly our results related to a symmetric operator
(depending on one parameter). We show that this operator has a unique fixed
point, which is repeller. Moreover, in the case of non-zero parameter, it has
two 5-periodic orbits. We divide the simplex to four subsets: the first set
consists a single point (the fixed point); the second (resp. third) set is the
set of initial points trajectories of which converge to the first (resp.
second) 5-periodic orbit; the fourth subset is the set of initial points
trajectories of which do not converge and their sets of limit points are
infinite and lie on the boundary of the simplex. We give interpretations of our
results to CFEP.
