Simple jerk systems are very useful for combining analytical computations and dynamical analysis in phase space. This is particularly relevant since there is still no direct link between the algebraic structure of ordinary differential equations and the topology of the chaotic attractors which they generate. In this paper, particular analytical solutions are identified for three simple chaotic flows. It is shown that these solutions have varying effects on the bifurcation diagrams. Moreover, a feedback circuit analysis is used to exhibit the similarities between the three simple systems. Such analysis also exhibits the relevant role of double nullcline in the topology of the attractor.