Elementary quadratic chaotic flows with no equilibria

Three methods are used to produce a catalog of seventeen elementary three-dimensional chaotic flows with quadratic nonlinearities that have the unusual feature of lacking any equilibrium points. It is likely that most if not all the elementary examples of such systems have now been identified.

► Some chaotic flows have the unusual feature of lacking any equilibrium points.
► Three methods are used to produce a catalog of seventeen simple chaotic flows.
► Our search was limited to three-dimensional flows with quadratic nonlinearities.