Elementary Bifurcation Theory
In general, bifurcation theory is concerned with dynamical systems which contain one, or more, external parameters, and with the manner in which the solution set may undergo structural changes as the parameter, or parameters, are varied. As we shall see, such behaviour is essentially determined by the stability of solutions and the manner in which this may change as the parameter, or parameters, vary. In this chapter we shall give an elementary and introductory account of bifurcation theory. For more advanced accounts the reader is referred to the texts by Chow and Hale (1982), Guckenheimer and Holmes (1983), and Iooss and Joseph (1980).