Multistability, multiperiodicity, multichaos: in a unified framework

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.