Page 521 - Mathematical Techniques of Fractional Order Systems

Characteristics
2 0:0138Þ
Main
LEs:ð0:0138; 0;
&
Properties
(0,5,0)
a 5 1:0
ICs:
Nonlinearities
3
–1
–2
–3
2
1
0
4
z
0 –4 system. conservative A 4 3 2 1 0 –1 –2 4 2 x y 4.5 1) 0.4, (0, ICs: 4 3.5 3 a 5 0:35 2.5 z 2 2 1:5008Þ LEs:ð0:0776; 0; 1.5 1 0.5 0 0 –1 –2 –3 –4 2 1 0 -1 x y 1 (1,1,-1) ICs: 0.5 0 a 5 1:0 –0.5 z –1 –1.5 (0.0522,0,-2.6585) LEs: –2 –2.5 –3 2 0 –2 –4 –6
Quadratic 4 3 2 1 0 z –1 –2 –3 –4 –2 –4 4.5 4 3.5 3 2.5 z 2 1.5 1 0.5 0 -2 1 0.5 0 –0.5 z –1 –1.5 –2 –2.5 –3 –3 150 100 z 50 0 –50 –40–20 0 1 0.5 0 z –0.5 –1 –1.5 –2 –2 –3
and 4 3 2 0 –1 2 0 0 –5 3 2 1
Equilibria Attractor 1 0 –1 –2 x –2 –3 –4 x –2 –4 –6 x –10 –15 –20 –25 x 0 –1 –2 x
No 4 2 0 y –2 –4 2 1 0 y –1 –2 2 1 0 y –1 –2 –3 –8 140 120 100 80 60 y 40 20 0 –20 –40 2 1 0 y –1 –2 –3
With
Attractors
Hidden Equations y 52 x 2 zy z 5 y 2 2 a z 5 2y 2 1 xz 2 a z 52 y 1 0:1x 2 1 1:1xz 1 a x 52 0:1y 1 a z 5 xz 2 3y y 52 2x 2 z z 52 y 2 1 z 2 1 a
17.1 x 5 y _ _ _ _ x 52 y _ y 5 x 1 z _ _ x 5 y _ y 5 z _ _ _ y 5 x 1 z _ x 5 2y _ _ _
TABLE (1) (2) (3) (4) (5)