  The system of two resources $R_1$, $R_2$ and one consumer $C$ is investigated
within the Rosenzweig-MacArthur model with Holling type II functional response.
The rates $\beta_i$ of consumption of resources $i=1,2$ are coupled by the
condition $\beta_1+\beta_2=1$. The dynamic switching is introduced by a
maximization of $C$: $d\beta_1/dt=(1/\tau) dC/d\beta_1$, where the
characteristic time $\tau$ is large but finite. The space of parameters where
both resources coexist is explored numerically. The results indicate that
oscillations of $C$ and mutually synchronized $R_i$ which appear at
$\beta_i=0.5$ are destabilized for $\beta_i$ larger or smaller. Then, the
system is driven to one of fixed points where either $\beta_1>0.5$ and
$R_1<R_2$ or the opposite. This behaviour is explained as an inability of the
consumer to change the preferred resource, once it is chosen.
