ABSTRACT
Graphical analysis lead us to deeper intuition about ordinary differential equations (ODEs) by enabling us to identify stable and unstable states, to plot dynamics, and to consider the effects of varying initial conditions and parameter values, rapidly and without any need for a computer. Changing the values of key parameters in an ODE can have a dramatic effect on the dynamics of system, and graphical methods can powerfully illustrate the effects. Graphical analysis enables us to quickly visualize the results of changing initial conditions or parameters, much like previous Boolean analysis. The chapter explores accompany ODEs, but like the Boolean approach, able to examine many responses simultaneously to obtain an idea of how the system works in general. It also relax some of the assumptions required to make analytical solutions of ODEs tractable; that the messenger RNA concentration reaches a steady state before the protein concentration.
