ABSTRACT
The objective of bifurcation theory is to investigate what happens to the type, number, and stability of the steady states as a result of a continuous change in some (or all) of the system parameters. The motivation for such analysis stems from the fact that in many real life situations the values of the model parameters are not known accurately or might actually be slowly varying functions of time which we approximate by constants to simplify the model Equations. This chapter presents some examples of "real life" bifurcations, which includes phase transitions, earthquakes, buckling of columns, magnetic hysteresis and so on. There is no universal agreement about the definition of chaos. Atmospheric flow in general is governed by a set of complicated nonlinear partial differential Equations. These Equations, which are called "Lorenz Equations", since their discovery have played a major role in the theory of nonlinear dynamical systems.
