This Letter contains three parts. First, it analyzes some basic properties of a new complex four-dimensional (4D) continuous autonomous chaotic system, in which each equation contains a cubic cross-product term. The new system has 9 equilibria, which display graceful symmetry with respect to the origin and the coordinate planes, and they have similarity associated with their linearized characteristics and along with invariant manifolds. Second, under constant control, the system displays (i) two coexisting symmetric double-wing chaotic attractors simultaneously, and (ii) two coexisting asymmetric double-wing and two coexisting single-wing attractors including chaotic, period-doubling, and periodic orbits. The evolution process of an attractor from double-wing to single-wing is investigated via a distribution diagram of equilibria and bifurcation diagrams of the system states. Finally, several circuits are built for different configurations of the new system, which show a good agreement between computer simulations and experimental results, revealing some important distinctions in applications arising from different frequencies used.
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