The system of two resources and 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 , 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.
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