  It is shown that periodic orbits can occur in Cholette's bioreactor model
working under the influence of a PI-controller. We find a diffeomorphic
coordinate transformation that turns this controlled enzymatic reaction system
into a generalized Lienard form. Furthermore, we give sufficient conditions for
the existence and uniqueness of limit cycles in the new coordinates. We also
perform numerical simulations illustrating the possibility of the existence of
a local center (period annulus). A result with possible practical applications
is that the oscillation frequency is a function of the integral control gain
parameter

Chaotic Dynamics