Prototypes of attractors in four dimensions

We study an extension of Duffing’s equation to three variables with external forcing. Starting from a phase-space preserving chaos, three prototypes of chaotic attractors with a dimension larger than three can be derived. We provide examples of hyperchaos and a ‘‘bifractal’’ in a four-dimensional flow. The second-order Poincaré cross section of hyperchaotic flow is qualitatively equivalent to the first-order cross section of Ueda’s attractor with the same forcing.