# Steady States for a Dynamical System in 2D

Steady States for a Dynamical System in 2D

Consider a hypothetical dynamical system governed by the following equations:

x

t

f

1

z

1

2

y

y

t

f

2

z

2

where and are bifurcation parameters that vary between and and with values set by the user.

z

1

z

2

-2

+2

The steady states of this system are solutions of the following system of equations:

f

1

z

1

2

y

f

2

z

2

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 (x,y) and (x,y) and the intersection points (shown in black), this Demonstration provides the numerical values of all roots for and .

f

1

=0

f

2

=0

-10≤x≤10

-10≤y≤10