Applying a constant voltage across an external resistor in series with, an electrochemical cell allows the continuous variation of the experimental control mode from potentiostatic to galvanostatic. The model for electrochemical pattern formation presented for potentiostatic conditions in Ref. 1 is extended to account for this general case. The resistor introduces a global coupling into the model, interacting in a nontrivial manner with the nonlocal coupling through migration currents in the electrolyte which occur independently of the control mode. The complex interplay of these two coupling terms is investigated as a function of operating parameters, and is illustrated by simulations in the bistable regime of an electrochemical reaction.