Many engineering problems can only be resolved by driving a chaotic attractor
in a periodic orbit.
As noted, the complexity of the chaotic attractor
under real-time information is smaller than that under only historical or combined historical and realtime information.
The trajectories of chaotic attractor
are swirling around one of the two equilibrium points in Figure 4.
The phase diagrams listed in Figure 1 show that the chaotic attractor
trajectory has ergodicity and boundedness in a specific attraction domain.
Caption: Figure 10: Two-dimensional projections ([x.sub.1] - [x.sub.2]) of five coexisting attractors for [a.sub.2] = 2.71 (a pair of chaotic attractors
, a pair of period-1 limit cycle, and a symmetric chaotic attractor
) with the rest of system's parameters as follows: b = [a.sub.1] = 3, [a.sub.0] = 1.75, [a.sub.3] = 1, [a.sub.4] = 0.0054.
This work follows  and adopts [[beta].sub.3] = 4.5 with chaotic attractor
in continuous-time and Poincare map shown in Figure 4.
Under different gear damping ratio [zeta] = 0.001, 0.02, 0.06 and 0.1, chaotic attractor
is not the same shape, as shown in Fig.
Figure 3(b) shows the routes to chaos of the system (2), and the system transforms into two-scroll hyperchaotic attractor from one-scroll chaotic attractor
. When the circuit parameter [rho] increases further, the system transforms into three-scroll hyperchaotic attractor from two-scroll hyperchaotic attractor.
The stable region, bifurcation, and chaos will be investigated; meanwhile, the largest Lyapunov exponent, entropy, chaotic attractor
, and the time domain response will be discussed to verify the dynamic characteristics of this system.
At the mature stage of a hurricane, direct estimation of the leading Lyapunov exponent using an axisymmetric model reveals, nevertheless, the existence of a chaotic attractor
in the phase space of the hurricane scales.
Lorenz found the first chaotic attractor
 in a three-dimensional autonomous system.
Ueta, "Yet Another Chaotic Attractor
", International Journal on Bifurcation and Chaos, Vol.