Page 492 - Mathematical Techniques of Fractional Order Systems

Dynamics, Synchronization and Fractional Order Form Chapter | 16 479

(A) (B)
1.6 1.5
1.4
1
1.2
0.5
1
y z
0.8
0
0.6
−0.5
0.4
0.2 −1
−1.5 −1 −0.5 0 0.5 1 1.5 −2 −1 0 1 2
x x
(C)
1.5
1

0.5
z
0
−0.5

−1
0 0.5 1 1.5
y
FIGURE 16.2 Chaotic attractors of system with infinite equilibria (16.10) in (A) x 2 y plane,
(B) x 2 z plane, and (C) y 2 z plane for a 5 0:1, b 5 0:1, c 5 1 and initial conditions
ðxð0Þ; yð0Þ; zð0ÞÞ 5 ð0:1; 0:1; 0:1Þ.

2

1
z
0

−1
2
2
1
y 0
0 −2 x
FIGURE 16.3 Chaotic attractor of the system in x 2 y 2 z space for a 5 0:1, b 5 0:1, c 5 1 and
initial conditions ðxð0Þ; yð0Þ; zð0ÞÞ 5 ð0:1; 0:1; 0:1Þ.