Page 523 - Mathematical Techniques of Fractional Order Systems

2 3:4341Þ
2 0:1Þ
LEs:ð0:0280; 0;
ICs:ð0; 3;
a 5 0:75
1
1.5
0
–0.5
0.5
3
2.5
2
z
0.5 6 5 4 3 2 1 0 –1 –2 2.5 2 1.5 1 x y 2 ICs:ð0; 2:3; 0Þ 0 –2 a 5 2:0 z –4 2 6:8524Þ LEs:ð0:0252; 0; –6 –8 4 2 0 –2 –4 –6 –8 –10 3 2 1 0 –1 x y 30 ICs:ð0; 0:1; 0Þ 25 20 a 5 1:3 15 z 10 2 10:2108Þ LEs:ð0:0314; 0; 5 0 3 2 1 0 –1 –2 –3 6 4 2 0 x y 2 ICs:ð0:5; 0; 0Þ 1.
–2 –1 0
0 –2
–3 –0.3 –0.2 –0.1 0 –1.5
–0.5 –4 –4 –1.5 –1 –0.5
–1 –6 –2
3 2.5 2 1.5 1 0.5 0 –0.5 2 0 –2 –4 –6 –8 –5 30 25 20 15 10 5 0 2 1.5 1 0.5 0 –0.5 –1 0.5 0 –0.5 –1 –1.5 –2 –2.5 –3 3 2 1 0 –1 –2
z z z z z z
4
6 3 2.5
2 3 0.6
5
2 2
4 0 2 0.4 1 1.5
3 1
–2 0
2 x x 0 x 0.2 x x 1 x
–4
1 0 –1 0.5
–6 –1
0 –2 –2 0
–1 –8 –0.2 –3
–2 –10 –3 –0.5
2.5 2 1.5 1 0.5 0 –0.5 –1 3 2 1 0 –1 –2 –3 –4 –5 6 4 2 0 –2 –4 –6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2 –0.3 0.5 0 –0.5 –1 –1.5 –2 2.5 2 1.5 1 0.5 0 –0.5 –1 –1.5
y y y y y y
z 52 y 2 xz 2 yz 2 a z 52 0:8x 2 1 z 2 1 a z 5 xy 1 0:5x 2 2 a z 52 xz 1 7x 2 2 a z 52 0:9y 2 xy 1 xz 1 a z 5 z 2 2xy 2 1:8xz 2 a
x 5 y _ y 5 z _ _ _ x 5 y _ y 52 x 1 z _ x 5 y _ y 52 x 2 yz _ _ _ x 5 y y 52 x 2 yz _ _ x 5 z _ y 5 z 2 y _ _ _ x 5 y _ y 52 x 1 z _
(6) (7) (8) (9) (10) (11)