The establishment and spread of invasive or nonindigenous species has caused concern from stakeholders in affected areas, and has prompted many field and modeling studies. We used stochastic two species, circular three patch dynamic models to investigate the patterns of invasion and impacts upon the affected species. Both persistent and degradable toxicants were incorporated as parts of the model system to act as disturbance regimens. There is a clear series of patterns that result from these simulations. Competition increases population variability, but decreases the number of distinct outcomes possible from the same initial conditions. Isolation of the patch of the introduction was the main determinant of successful establishment through a process we call the beachhead effect. Coexistence of species was often possible in local patches, contrary to the analytical solutions of Lotka-Volterra equations and numerous modeling studies. Contaminants and their resultant disturbances are important as contributors to the stochastic nature of models. The stochasticity leads to a variety of outcomes from some sets of initial conditions. Different outcomes have different probabilities of occurrence and are dependent upon the specific initial conditions of the simulation. A clear pattern that is apparent is the “beachhead effect,” where the invasive establishes a population within a relatively remote patch before migrating to the remainder of the landscape. We make predictions and provide specific research hypotheses as to the causes and effects of invasive species establishment, spread, and impacts.