Consider a hypothetical dynamical system governed by the following equations:
where and are bifurcation parameters that vary between and and with values set by the user.
The steady states of this system are solutions of the following system of equations:
The above system of two nonlinear equations exhibits multiple solutions that can all be determined using the built-in Mathematica function ContourPlot . In addition to giving a graphical representation of the contours and and the intersection points (shown in black), this Demonstration provides the numerical values of all roots for and .