The parameter-space of the three-parameter A2 symmetric flow

•We consider the three-parameter A2 symmetric flow model.•We consider three two-dimensional cross sections of their parameter-space.•Periodic structures embedded in a large chaotic region are found.•These periodic structures are organized themselves in different ways.

Three two-dimensional parameter planes of a three-parameter, three-dimensional set of autonomous nonlinear first-order differential equations used to model the A2 symmetric flow are investigated. This is done by using the three two-dimensional cross sections of the three-dimensional parameter-space generated by the model. We show that regardless of the two-parameter set considered in the parameter plane plots, all the diagrams present periodic structures embedded in a large chaotic region. We also show that these periodic structures organize themselves in different ways, including sequences whose periods have a well-defined law of formation that can be written in a closed form, and sequences organized in period-adding bifurcation cascades.