Sudden changes in
chaotic attractors and transient basins in a model for rattling in gearboxes, Chaos, Solitons and Fractals 21(3): 763-772.
Here, the verification for the WPAC basin is presented because of the larger sample size of strong storms that will facilitate our subsequent analysis of the MPI limit and
chaotic attractor.
By building the complete bifurcation diagrams with stable and unstable periodic solutions, we have found different new bifurcation groups with their own rare regular and
chaotic attractors.
Chaotic attractors are significant at every stage in this process because, as part of their expanding phase, they lend the capacity to rapidly generate endlessly new activity patterns or potential complexes of meaning, thereby creating information (Nicolis and Tsuda 216).
Convergence of the point estimates of the GP correlation dimensions to a single number would provide evidence of the existence of a
chaotic attractor.
A
Chaotic Attractor for the S&P 500," Financial Analysts Journal, 47(2): 55-62.
What Hunt fails to point out, however, is that predictability fails for two distinct reasons in nonlinear systems: (1) arbitrarily close points on the same
chaotic attractor will diverge over time in an exponential fashion, and this divergence occurs within a single stable state of the system; (2) nonlinear systems may have more than one stable final state, and arbitrarily close initial conditions may diverge to different stable states, and these states may be chaotic or periodic.
Chaotic attractors are neither novel nor recurrent; they have the same number of isometries as their shuffled copies (Figure 5).
Given that such sporadic shocks are not uncommon in foreign exchange markets, a grandiose aspiration of finding a long-term steady-state dynamical path by locating a
chaotic attractor would be impractical.
Effectively, there are circumstances in which we expect the basin of the
chaotic attractor to effectively disappear, because it intersects the alternative basin; hence the term basin boundary collision.
It's sufficient to observe the system long enough to map its
chaotic attractor and to determine by experiment a few crucial quantities necessary for establishing control.
The
chaotic attractor was formally proposed by Ruelle and Takens in 1971 and the nonperiodic flow appearing in the dissipative system was called the strange attractor by them [1].
