Page 529 - Mathematical Techniques of Fractional Order Systems

(0,0,0).
at
point
characteristics
equilibrium
nonlinearities.
LEs:ð0:0377; 0; 2 2:0377Þ
stable
main
Quadratic
single
&
ICs:ð4; 2 2; 0Þ
Properties
A

–1 6 5 4 3 2 1 0 y ICs:ð0; 0:5; 0:5Þ LEs:ð0:0717; 0; 2 0:5232Þ nonlinearities. Quadratic i.e., system, this of equilibrium line the is z-axis The equilibria. other no with ð0; 0;zÞ 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 y ICs:ð0; 3:9; 0:7Þ ParameterðÞ:a 5 8:888; b 5 4 s nonlineariti
–2 0 –1 –2
4 3 2 1 0 –1 –2 –3 –4 0.5 –0.5 –1.5 10 5 0 –5 –10
z z z
10 1.5
0.4
8 1
Types 6 4 x 0.2 0 x 0.5 0 x
Various 2 0 –0.2 –0.4 –0.5 –1 –1.5
of Attractor 6 5 4 3 2 y 1 0 –1 –2 –2 0.6 0.4 0.2 0 y –0.2 –0.4 –0.6 –0.6 5 0 y –5 –10
Attractors
Hidden
Further z 52 x 2 0:6y 2 2z 1 z 2 2 0:4xy z 52 x 2 15xy 2 xz z 5 z 1 ax 2 2 y 2 2 b
17.2 Equations _ x 5 y _ y 5 z _ _ x 5 y _ y 52 x 1 yz _ x 5 y _ y 52 x 1 yz _ _
TABLE (19) (20) (21)