Steady States for a Dynamical System in 2D

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 [1]. 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 .