Two counterexamples to Aizerman's conjecture

In the last few years, several sufficient conditions have been found for establishing the asymptotic stability in the large of the null solution of feedback systems containing a single non-linearity. The experiments reported in this paper show that, if these sufficient conditions are violated, in certain cases instability occurs in the form of oscillations. These experiments not only establish a new class of oscillators but they also constitute counterexamples to Aizerman's conjecture. An explanation of the oscillations is proposed which uses harmonic linearization.