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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 .

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Reference
[1] S. Wagon, Mathematica in Action: Problem Solving through Visualization and Computation, 3rd ed., Berlin: Springer–Verlag, 2010.
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