Modeling the nonlinear interactions between flow, sediment, and vegetation is essential for improving our understanding and prediction of river system dynamics. Using simple numerical models, we simulate the key flow-sediment-vegetation interaction where the disturbance is intrinsically generated by the presence of vegetation. In this case, biomass growth modifies the flow field, induces bed scour, and thus potentially causes vegetation uprooting when erosion exceeds root depth. Our results show that this nonlinear feedback produces deterministic chaos under a wide range of conditions, with complex aperiodic dynamics generated by a period-doubling route to chaos. Moreover, our results suggest relatively small values of Lyapunov time, spanning 2-4 growth-flood cycles, which significantly restrict the predictability of riverbed evolution. Although further spatial and temporal processes may add complexity to the system, these results call for the use of ensemble methods and associated uncertainty estimates in ecomorphodynamic models.