Abstract. Of the eight types of hyperbolic equilibrium points in three-dimensional flows, one is overwhelmingly dominant in dissipative chaotic systems. This paper shows examples of chaotic systems for each of the eight types as well as one without any equilibrium and two that are nonhyperbolic. The systems are a generalized form of the Nosé–Hoover oscillator with a single equilibrium point. Six of the eleven cases have hidden attractors, and six of them exhibit multistability for the chosen parameters.