Modelling growth of drug resistant cancer populations as the system with positive feedback

We are concerned with dynamical properties of models of emergence of resistance of cancer cells to chemotherapy, based on recent progress in molecular biology. The model of the process has a form of the infinite system of linear and bilinear state equations. We show that, it can be decomposed into two parts: the first one is finite dimensional bilinear, and the second one is infinite dimensional linear, coupled by the positive feedback. Then, we use some results of the theory of feedback systems to study the asymptotic properties of the process.