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In-Depth Information
Fig. 2.4
Isoclines diagram
for s.x/ D
5
sin.x
1
/
x
2
c=−1/4
c=−1/3
c=−1/2
c=−1.0
c=1.0
c=1/2
c=1/3
c=1/4
4
3
2
1
0
−1
−2
−3
−4
−5
−5
0
5
x
1
Fig. 2.5
Isoclines diagram
for s.x/ D
5
0:5x
2
sin.x
1
/
x
2
c1=−3/4
c2=−5/6
c3=−1
c4=−3/2
c5=1/2
c6=0
c7=−1/6
c8=−1/4
4
3
2
1
0
−1
−2
−3
−4
−5
−5
0
5
x
1
Example 2.
The following oscillator model is considered, being free of friction and
with state-space equations
x
1
D x
2
x
2
D0:5x
2
sin.x
1
/
(2.31)
To compute isoclines one has
0:5x
2
sin.x
1
/
s.x/ D
x
2
D c)0:5x
2
sin.x
1
/ D cx
2
)
.0:5 C c/x
2
D sin.x
1
/)x
2
D
(2.32)
1
0:5Cc
sin.x
1
/
For different values of parameter c the isoclines are depicted in Fig.
2.5
.
