The effect of external magnetic perturbations (MPs) on the helical self-organization in nonlinear three-dimensional magnetohydrodynamic modelling of fusion plasmas is discussed. The tokamak, stellarator and reversed-field pinch (RFP) toroidal configurations for magnetic confinement are considered. In the case of current-carrying RFP and tokamak plasmas, MPs are predicted to stimulate the bifurcation to long-lived helical states, as confirmed by experimental observations in the RFX-mod device. For all the configurations, the effect of MPs on the magnetic topology is discussed and interpreted on the basis of the safety factor profile computed by taking into account the dominant helical component of the magnetic field.