In previous work, we introduced a minimal model of the alternative pathway of the complement. We also limited our analysis to a reduced set of parameter values because, for some parameters, experimentally supported estimates were not found. On the other hand, changes in value of some parameters may be a result of a pathological condition. Therefore, here we extend our analysis and include a wider range of values of five of the physiologically relevant parameters. For all the parameters considered, we observe chaotic oscillations, and we construct bifurcation diagrams using Poincaré sections of local maxima.