Page 531 - Mathematical Techniques of Fractional Order Systems

Case 2 ICs:ð0; 0:01; 0:01; 0Þ nonlinearities. quadratic and Hyperbolic 1 0.5 a 52 0:05 0 1: Case –0.5 ParameterðÞ:b 5 0 s –1 w-axis. along equilibrium Line –1.5 LEs:ð0:029; 0:0088; 0; 2 0:1151Þ 0.8 0.6 0.4 0.2 0 –0.8 –0.6 –0.4 –0.2 2: Case x ParameterðÞ:b 52 0:001 s 3 equilibria. No 2 LEs:ð0:02
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 _

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