A Large Chaotic Region in a 3-D Sinusoid Discrete Map

We investigate in this paper a new simple 3-D sinusoid discrete map with two nonlinearities has an important property, in which the all orbits of this map are bounded, and can describe Lorenz-type chaotic attractors form a reverse period-doubling bifurcation scenario route to chaos. The property of bounded orbits permits the existence of large chaotic region of the proposed map when one parameter bifurcation continually increasing.