Instability of oscillations in the Rosenzweig–MacArthur model of one consumer and two resources

The system of two resources $R1$ and $R2$ 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 $Ri$⁠, 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.