We have used global MHD simulations to investigate the magnetospheric response to steady solar wind for two events. The event of 18 April 2002 is characterized by periodic particle injections and magnetic field dipolarizations, or sawtooth activity, at geosynchronous orbit, while 3-4 February 1998 is a period of steady magnetospheric convection (SMC). In our simulations we find for both events that a general system of convection develops, characterized in the magnetotail by large-scale sunward flows driven by reconnection in region of 30-45 RE downstream. These flows in general divert around the inner magnetosphere to the dawn and dusk flanks and then converge toward the dayside magnetopause. In the sawtooth event we find reconnection is intermittent and patchy, resulting in flow bursts which on average produce the general convection pattern indicated, but a fraction of them penetrate into the inner magnetosphere and are associated with observed plasma injections and field dipolarizations. In the SMC event the convection system is formed by quasi-steady reconnection in the midtail, which drives steady earthward flows. These flows divert to the flanks, leaving the inner magnetosphere undisturbed. We find the difference in the magnitude of IMF B-Z is unlikely to account for difference in activity in the two events, as a simulation of the SMC event with increased vertical bar B-Z vertical bar produced qualitatively the same steady convection. Solar wind density variations are shown to control the average mass transport but have no correlation with the flow channels responsible for the inner magnetospheric activity in the simulations.