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Dual Combination Synchronization Scheme Chapter | 12 357

40
100
30 50
x 33 (t) 20 x 34 (t) 0
10 –50
0 –100
20 20
20 20
0 0
0 0
–20 –20 –20 –20
x (t) x (t)
32 –40 –40 (t) 32 –40 –40
x 31 x (t)
31
(A) (B)
100
100
50 50
x 34 (t) 0 x 34 (t) 0
–50 –50
–100 –100
40 40
30 20 30 20
20 0 20 0
10 –20 (t) 10 –20
x (t) x 33
33 0 –40 0 –40
x (t) x (t)
31 32
(C) (D)
FIGURE 12.5 Phase portraits of Lu hyperchaotic system for α 5 0:95 (A) in x 31 2 x 32 2 x 33 ,
space (B) in x 31 2 x 32 2 x 34 space, (C) in x 31 2 x 33 2 x 34 space, (D) in x 32 2 x 33 2 x 34 space.
x 32 2 x 33 2 x 34 spaces are depicted through Fig. 12.5 for α 5 0:95 at
a 31 5 36; a 32 5 3; a 33 5 20, and a 34 52 1.

α
d y 31
dt α 5 b 31 y 31 2 y 32 1 u 21
α
d y 32 2
33
dt α 5 y 31 2 y 32 y 1 u 22
α ð12:15Þ
d y 33
dt α 52 b 32 y 32 2 b 33 y 33 2 b 34 y 34 1 u 23
α
d y 34 5 y 33 1 b 35 y 34 1 u 24 ;
dt α

where u 21 ; u 22 ; u 23 ; u 24 ; are control functions, y 31 ; y 32 ; y 33 , and y 34 are
states variables and b 31 ; b 32 ; b 33 ; b 34 , and b 35 are the constant parameters.
The phase portraits of (12.15) in y 31 2 y 32 2 y 33 , y 31 2 y 32 2 y 34 ,
y 31 2 y 33 2 y 34 , y 32 2 y 33 2 y 34 spaces are depicted through Fig. 12.6 for
α 5 0:95 at b 31 5 0:56; b 32 5 1:0; b 33 5 1:0; b 34 5 6:0, and b 35 5 0:8.