A cellular automata model was developed and parameterized to test the effectiveness of application of biological control insects to water hyacinth (Pontederia crassipes), which is an invasive floating plant species in many parts of the world and outcompetes many submersed native aquatic species in southern Florida. In the model, P. crassipes was allowed to compete with Nuttall’s waterweed (Elodea nuttallii). In the absence of biocontrol acting on the P. crassipes, E. nuttallii excluded P. crassipes at low concentrations of the limiting nutrient (nitrogen), and the reverse occurred at high nutrient concentrations. At intermediate values, alternative stable states could occur; either P. crassipes alone or a mixture of the two species. When the biocontrol agent, the weevil Neochetina eichhorniae, was applied in the model, there was initially a rapid reduction of the P. crassipes, however, over time a regular striped pattern of moving spatially alternating stripes of P. crassipes and E. nuttallii emerged. -This pattern of moving stripes emerged and persisted over thousands of days but could quickly transform into an irregular pattern at some apparently random time, when either external stochasticity (added adult weevils) or only the weak internal stochasticity of weevil movements occurred. The cause of the end of the long transient can be traced to a single slightly irregular pixel within the striped pattern. Model parameters were varied to study effects of plant growth rate, nutrient concentration and nutrient diffusion rate on the dynamics of the system.