The system of two resources R and R and one consumer C is investigated within the Rosenzweig-MacArthur model with a Holling type II functional response. The rates of consumption of particular resources are normalized as to keep their sum constant. Dynamic switching is introduced as to increase the variable C in a process of finite speed. The space of parameters where both resources coexist is explored numerically. The results indicate that oscillations of C and mutually synchronized R, which appear equal for the rates of consumption, are destabilized when these rates are modified. Then, the system is driven to one of fixed points or to a limit cycle with a much smaller amplitude. As a consequence of symmetry between the resources, the consumer cannot change the preferred resource once it is chosen.