[en] Resistive kink oscillations in tokamak plasmas are usually treated as core localized events, yet there there are several mechanisms by which they may interact with the edge dynamics. This suggests that we may regulate edge oscillatory behaviour, or ELMs, by harnessing the natural or contrived sawtooth period and amplitude. In this work I investigate core-edge oscillatory entrainment through direct propagation of heat pulses, inductive coupling, and global higher order resonance effects. In the core of auxiliary heated tokamak plasmas the ineluctable rhythm of slow buildup and rapid conversion of potential energy governs electron and heat radial transport. The growth phase of the sawtooth is accompanied by significant reconnection, then during the collapse the temperature and density in the core fall dramatically. There is evidence from experiments in reversed field pinch devices that ensuing energy fluxes can affect flow shear and confinement at the edge. The basis for this study is the dynamical (BDS) model for edge plasma behavior that was derived from electrostatic resistive MHD equations. The BDS model reflects the major qualitative features of edge dynamics that have been observed, such as L-H transitions and associated ELMs, hysteresis, and spontaneous reversal of poloidal shear flow. Under poorly dissipative conditions the transient behavior of the model can exhibit period-doubling, blue-sky, homoclinic, and other exotic bifurcations. Thus we might ask questions such as: Is it possible to mode-lock the edge dynamics to the core sawteeth? Can we induce, or prevent, a change in direction of shear flow? What about MHD effects? Is core-edge communication one way or is there some feedback? In the simplest prototype for coupled core-edge dynamics I model the sawtooth crash as a periodic power input to the edge potential energy reservoir. This is effected by coupling the BDS model to the dynamical system u = u(1 - u² - x²) - ω_sx, x = x(1-u² -x²) + ω_su, which has an asymptotically stable periodic solution (u(t), x(t)) = (cos(ωt + θ), sin(ωt + θ)), where ω_s is the sawtooth frequency and θ is an arbitrary phase shift. There is a spontaneous reversal of shear flow before the dynamics can settle onto a limit cycle in the negative shear flow domain. We see that a periodic power input can suppress this reversal. In further work to be presented it is shown that inductive and MHD coupling can also modulate the edge dynamics, and examples are given of sawtooth-controlled ELMs and confinement transitions. (author)