chaotic attractor

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Related to chaotic attractors: Basin of attraction, Chaotic dynamical systems
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Noun1.chaotic attractor - an attractor for which the approach to its final point in phase space is chaotic
attracter, attractor - (physics) a point in the ideal multidimensional phase space that is used to describe a system toward which the system tends to evolve regardless of the starting conditions of the system
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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.
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.