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Steady States for a Dynamical System in 2D

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Consider a hypothetical dynamical system governed by the following equations:

[more]

,

,

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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Contributed by: Brian G. Higgins and Housam Binous (June 2011)
Open content licensed under CC BY-NC-SA

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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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