Page 526 - Mathematical Techniques of Fractional Order Systems

Characteristics

Main 2 2:0398Þ -2.1282) 2 11:8580Þ

& 2 1Þ 0, LEs:ð0:1101; 0; 2 1:3879Þ LEs:ð0:0607; 0; 2 0:1883Þ
Properties ICs:ð0:5; 0; a 5 0:1 LEs:ð0:0654; 0; ICs:ð2:5; 0; 0Þ a 5 0:4 (0.1028, LEs: ICs:ð1; 0; 2 4Þ a 5 1:0 LEs:ð0:0532; 0; ICs:ð0; 1; 2 4:9Þ a 5 1:0 ICs:ð0; 1; 2 1Þ a 5 1:0

1 2 0 0
3
0
0 –2
–1 –5 2
–2 –4
–2 x x –10 x x 1 x
–3 –4 –15 –6 0
–4 –6 –8
–5 –20 –1
–8 –10
12 10 8 6 4 2 0 –2 –4 10 5 0 –5 10 5 0 –5 –10 –15 25 20 15 10 5 0 –5 –10 3 2 1 0 –1 –2 –2
z z z z z
10 8
0 8 6 10 6 4 3
–3.5 –3 –2.5 –2 –1.5 –1 –0.5 y 4 2 0 –2 y 5 0 –5 y 2 0 –2 –4 y 2 1 0 y
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)