STABILITY OF SOME TEST EQUATIONS WITH DELAY

The authors propose some techniques to obtain stability conditions for certain differential equations with delay. These techniques are applied to three concrete test situations. In the first and second cases, they consider equations without instantaneous dissipative terms. This is important because in real situations, such as control theory, finite time is necessary to measure characteristics of the object and to treat the results of the measurements in order to create control action. In the last section, general results are presented for the chemostat model. These test equations are interesting examples for a forthcoming investigation concerning stability of numerical methods.