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].