  In this paper, we present a unified framework of multiple attractors
including multistability, multiperiodicity and multichaos. Multichaos, which
means that the chaotic solution of a system lies in different disjoint
invariant sets with respect to different initial values, is a very interesting
and important dynamical behavior, but it is never addressed before to the best
of our knowledge. By constructing a multiple logistic map, we show that
multistability, multiperiodicity and multiple chaos can exist according to
different value of the parameter p. In the end, by the derived compact
invariant set of the Lorenz system, the multiple Lorenz chaotic attractors are
constructed using a sawtooth function.
