Oscillations in a CSTR Affected by the Pump Periodicity

Most experiments on chemical oscillations are executed in a CSTR, i.e. continuously stirred tank reactor. The reactants are usually fed into the reactor by means of a peristaltic pump. The pump does not work in a continuous manner, but, as its name implies, pushes the material in a wave-like manner. Thus one must assume that the flow into the reactor is not continuous but involves some time periodicity, which depends on the pump. The usual differential equations used in such problems are: $$ \dot{c} = R(c) + {k_0}\left( {{c_0} - c} \right) $$ where c is the vector of concentrations, R(c) is the vector of chemical rate terms, c0 is the vector of feed concentrations and k0 is the flow rate — taken usually to be a constant value.