Modelling chaos and hyperchaos with 3-D maps

Two generalizations on R3 of the Hénon nonconservative map are defined. Although, in many respects, they are closely related to each other, one of them can produce strange attractors with only one positive Lyapunov exponent, while the other has strange attractors with two positive Lyapunov exponents, thus showing a “hyperchaotic” behaviour. The results of numerical tests to be discussed, show, that apart from obvious differences in the number of positive Lyapunov exponents and the shape of the chaotic atractor, the hyperchaos may not be much different from regular chaos.