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WOLFRAM|DEMONSTRATIONS PROJECT

Steady States for a Dynamical System in 2D

​
contour plot
root list
representation of some roots
z
1
-1.05
z
2
0.1
Consider a hypothetical dynamical system governed by the following equations:
x
t
=
f
1
(x,y)=x-
z
1
2
y
cosy
,
y
t
=
f
2
(x,y)=-y+xsinx+
z
2
,
where
z
1
and
z
2
are bifurcation parameters that vary between
-2
and
+2
and with values set by the user.
The steady states of this system are solutions of the following system of equations:
f
1
(x,y)=x-
z
1
2
y
cosy=0
,
f
2
(x,y)=-y+xsinx+
z
2
=0
.
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
f
1
(x,y)
=0
and
f
2
(x,y)
=0
and the intersection points (shown in black), this Demonstration provides the numerical values of all roots for
-10≤x≤10
and
-10≤y≤10
.
​
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