Page 532 - Mathematical Techniques of Fractional Order Systems

(Continued)

nonlinearities.

quadratic w-axis. along

and equilibrium LEs:ð0:029; 0:0088; 0; 2 0:1151Þ LEs:ð0:0291; 0:0098; 0; 2 0:1152Þ
ICs:ð0; 0:01; 0:01; 0Þ Hyperbolic a 52 0:05 1: Case ParameterðÞ:b 5 0 s Line 2: Case ParameterðÞ:b 52 0:001 s equilibria. No

0.8 0.8 0.8
0.6 1 0.6 0.6
0.4 0.5 0.4 0.4
0.2 0.2 0.2
0
0 0
x y 0 x x
–0.8 –0.6 –0.4 –0.2 –0.5 –1 –0.8 –0.6 –0.4 –0.2 –0.8 –0.6 –0.4 –0.2
Case 2 1 0.5 0 –0.5 –1 –1.5 3 2 1 0 –1 –2 –1.5 3 2 1 0 7.4 7.2 7 6.8 6.6 6.4 6.2

y z z –1 –2 w
0.8 0.8 0.8
1
0.6 0.6 0.6
0.4 0.5 0.4 0.4
0.2 0.2 0.2
0
0 0 0
x –0.5 y x x
–0.8 –0.6 –0.4 –0.2 –1 –0.8 –0.6 –0.4 –0.2 –0.8 –0.6 –0.4 –0.2
Case 1 1 0.5 0 –0.5 –1 –1.5 2.5 2 1.5 1 0.5 0 –0.5 –1 –1.5 –2 –1.5 2.5 2 1.5 1 0.5 0 –0.5 –1 –1.5 –2 7.4 7.2 7 6.8 6.6 6.4 6.2

y z z w
x 52 x 1 1:6tanðxÞ 1 2tanhðyÞ 1 tanhðzÞ y 52 y 1 aw 2 tanhðxÞ 1 1:5tanhðyÞ z 52 z 1 3tanhðxÞ 2 2tanhðyÞ 1 tanhðzÞ 1 b

_ _ _ w 5 tanhðxÞ _
(22)