  There is one-to-one correspondence between quadratic operators (mapping
$\mathbb R^m$ to itself) and cubic matrices. It is known that any quadratic
operator corresponding to a stochastic (in a fixed sense) cubic matrix
preserves the standard simplex. In this paper we find conditions on the
(non-stochastic) cubic matrix ensuring that corresponding quadratic operator
preserves simplex. Moreover, we construct several quadratic non-stochastic
operators which generate chaotic dynamical systems on the simplex. These
chaotic behaviors are \emph{splitted} meaning that the simplex is partitioned
into uncountably many invariant (with respect to quadratic operator) subsets
and the restriction of the dynamical system on each invariant set is chaos in
the sense of Devaney.
