Summary: The chaotic behavior of the Rabinovich-Fabrikant system, a model with multiple topologically different chaotic attractors, is analyzed. Because of the complexity of this system, analytical and numerical studies of the system are very difficult tasks. Following the investigation of this system carried out in [third and fourth author, Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 10, 3409–3447 (2004; Zbl 1129.37314
)], this paper verifies the presence of multiple chaotic attractors in the system. Moreover, the Monte Carlo hypothesis test (or, equivalently, surrogate data test) is applied to the system for the detection of chaos.