Caption: Figure 3:
Chaotic attractors of system (1) with [[beta].sub.1] = 8.25, [[beta].sub.2] = 0.8, [[beta].sub.3] = 12.25, and [[beta].sub.4] = 0.2: (a) in [x.sub.1] - [x.sub.2] - [x.sub.3] space, (b) in [x.sub.1] - [x.sub.2] - [x.sub.4] space, (c) in [x.sub.1] - [x.sub.3] - [x.sub.4] space, and (d) in [x.sub.2] - [x.sub.3] - [x.sub.4] space.
Chaotic attractors of master system (26) are shown in Figure 1.
Chen, "Impulsive control of
chaotic attractors in nonlinear chaotic systems," Applied Mathematics and Mechanics, vol.
The threshold value is the associated dimension of the
chaotic attractor. The embedded dimension is the minimum embedded dimension which ensures that the topological structures of
chaotic attractors can be unfolded completely.
[30] solved the ultimate boundary problem of more existing
chaotic attractors and hyperchaotic attractors and got the numerical solutions of corresponding bounds.
The two- and three-dimensional
chaotic attractors with Matlab simulation of the modified Lorenz-like chaotic system (2) are shown in Figure 1.
Yorke, "The dimension of
chaotic attractors," in The Theory of
Chaotic Attractors, pp.
Since Lorenz found the first
chaotic attractor in a smooth three-dimensional autonomous system, considerable research interests have been made in searching for the new
chaotic attractors [1-14].
These systems can generate one-directional (1D) n-scrolls, two-directional (2D) n x m grid scroll, and three-directional (3D) nxmxl grid scroll
chaotic attractors by adding breakpoints in the PWL function and increasing the number of PWL functions into the nonlinear system [7, 8].
The NCS exhibits complex and abundant dynamics behaviors; see Figure 3 where
chaotic attractors are shown.
Caption: FIGURE 3: The
chaotic attractors of system (3) with a = 10, b = 40, c = 2.5, k = 2, h = 2, and l = 1.
By comparing black dots of Figure 5(a) and red dots of Figure 5(a), one can notice that system (1a), (1b), and (1c) displays coexistence of period-6-oscillations and
chaotic attractors in the range 3.182 < b < 3.188 and coexistence of period-3-oscillations and
chaotic attractors in the range 3.188 [less than or equal to] b < 3.2012.