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Fig. 2.11
Phase diagram of
state variables x
1
, x
2
of a
second order linear
autonomous system with
complex unstable eigenvalues
1
x 10
10
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−8
−6
−4
−2
0
2
4
6
8
x 10
9
x
1
Fig. 2.12
Phase diagram of
state variables x
1
, x
2
of a
second order linear
autonomous system with
imaginary eigenvalues
25
20
15
10
5
0
−5
−10
−15
−20
−25
−15
−10
−5
0
5
10
15
x
1
stability properties of nonlinear dynamical systems
x
1
D f
1
.x
1
;x
2
/
x
2
D f
2
.x
1
;x
2
/
(2.52)
which gives
x
1
D f
1
.p
1
;p
2
/ C ˛
11
.x
1
p
1
/ C ˛
12
.x
2
p
2
/ C h.o.t
x
2
D f
2
.p
1
;p
2
/ C ˛
21
.x
1
p
1
/ C ˛
22
.x
2
p
2
/ C h.o.t
(2.53)
