Mixotrophic nutrition, in which organisms combine aspects of heterotrophic and autotrophic nutrition, is a common characteristic of many harmful algae bloom (HAB) species. In this research we employ a numerical plankton model that reproduces seasonal succession dynamics to investigate how mixotrophic abilities and enrichment influence population dynamics. Results demonstrate that enrichment can generate chaos amongst yearly peak mixotroph densities. In some cases, the year-to-year peak mixotroph densities became erratic and highly variable. Further, we demonstrate that chaotic dynamics arise in the model system under a wide range of mixotroph life-history trait combinations. These results demonstrate, for the first time to our knowledge, that initiation of a mixotrophic HAB can occur with enrichment, due to erratic population spikes, when no role of broadcast allelopathy is considered. Had allelopathy been included as part of the model, it is likely that once the mixotroph population reached a threshold at which allelochemicals produce mass effects, the persisting algae populations would have been eliminated and the mixotroph bloom trajectory reinforced, reaching even higher population densities. These results help unify understandings of broadcast allelopathy in algal bloom formation. They may also shed light on why it is difficult to predict the occurrence of mixotrophic HABs based solely on environmental variables, when the year-to-year maximum density of the mixotroph is chaotic with enrichment.