Page 525 - Mathematical Techniques of Fractional Order Systems

Characteristics
2 2:0398Þ
Main
2 1Þ
LEs:ð0:0654; 0;
&
Properties
ICs:ð0:5; 0;
a 5 0:1
6
–2
0
2
4
12
10
8
z
–3.5 –3 –2.5 –2 –1.5 –1 –0.5 –4 1 0 –1 –2 –3 –4 –5 0 x y ICs:ð2:5; 0; 0Þ 10 5 a 5 0:4 z 0 -2.1282) 0, (0.1028, LEs: –5 2 0 –2 –4 –6 –8 10 8 6 4 2 0 –2 x y 10 ICs:ð1; 0; 2 4Þ 5 a 5 1:0 0 z –5 2 11:8580Þ LEs:ð0:0532; 0; –10 –15 0 –5 –10 –15 –20 10 5 0 –5 x y 25 I
12 10 8 6 4 2 0 –2 –4 10 5 0 –5 –4 10 5 0 –5 –10 –15 –10 25 20 15 10 5 0 –5 –10 –6 –8 3 2 1 0 –1 –2 –1 –2
z z z z z
1 2 0 0
3
0
0 –2
–1 –5 2
–2 –4
–2 –3 x –4 x –10 –15 x –6 x 1 0 x
Attractor 0 –0.5 –1 –1.5 y –2 –2.5 –3 –3.5 –4 –5 10 8 6 4 2 y 0 –2 –4 –6 –8 10 5 y 0 –5 –10 –20 8 6 4 2 0 y –2 –4 –6 –8 –8 –10 3 2 1 y 0 –1 –2 –1 –2
(Continued) z 52 4x 2 1 8xy 1 yz 1 a z 5 xy 1 xz 1 0:2yz 2 a z 5 x 2 2 y 2 1 2xz 1 yz 1 a z 5 x 2 2 y 2 1 xy 1 0:4xz 1 a x 52 0:8x 2 0:5y 2 1 xz 1 a y 52 0:8y 2 0:5z 2 1 yx 1 a z 52 0:8z 2 0:5x 2 1 zy 1 a
17.1 Equations x 5 z _ y 5 x 2 y _ _ _ x 52 y _ y 5 x 1 z _ x 5 y _ y 5 z _ _ _ x 5 y _ y 5 z _ _ _ _
TABLE (12) (13) (14) (15) (16)