ABSTRACT
In this introductory chapter we present some fundamental concepts associated with the stability of nonlinear systems. These issues include static multiplicity, dynamics associated with Hopf points, and the singularity theory as well as some numerical tools used to generate the bifurcation diagrams. The reader should be cautioned that the material in this chapter represents a scratch on the surface of these issues. Nevertheless, the material is presented in a simple and practical manner. The goal is to provide the reader with practical tools to study many of the nonlinear phenomena encountered in unstructured kinetic models of bioreactors. Some concepts and definitions, not directly needed in the materials presented in this chapter, are provided in the Appendix. Details about nonlinear systems and bifurcation theory can be found, for instance, in [136, 198, 237, 303, 315, 354, 366] while the singularity theory and some of its useful applications are available in [33, 39, 42, 43, 44, 45, 46, 70, 132, 133, 227]. Details about continuation techniques can, on the other hand, be found in [98, 134, 183, 192, 199, 315].
