Tripleurospermum perforatum is an invasive weedy species which exhibits strong over-compensating density dependence. Interactions between density-dependent survival, probability of flowering and fecundity were modelled and their impact on the population dynamics were examined. When only fecundity was density-dependent, the dynamics were similar to those observed in the model containing all three density-dependent terms. Density-dependent survival was a stabilizing process when acting in combination with density-dependent fecundity and probability of flowering; removing density-dependent survival from the model produced two-point cycles. The addition of a seed bank was also stabilizing. Simulations of control strategies at different life-history stages indicated that full control would be difficult due to the strong over-compensating density dependence, with severe reductions in fecundity and late season survival necessary in order to reduce equilibrium seed density and biomass.