Then, we reconstruct the phase space
and establish the first order linear prediction model.
To work in that many-dimensional phase space
, for example, astronomers need to learn what Loredo terms "a little nontrivial math.
Similar to Poincare's "point of intersection" in phase space
the dream suggests an equivalency to the midpoint between mind and matter where the magnetism occurs.
Multidimensional Phase Space
of Dispersed Oil Bubble and Slug Fluctuating Signals.
z], the entire wavefront corresponds to a 2-dimensional surface in the 6-dimensional phase space
, given by the conditions
When the one dimensional pixel intensity series transformed to an m dimensional phase space
, the information dimension can be used to measure the smoothness of the transformed phase space
The first step is to embed data in a higher dimensional phase space
With a properly selected time delay, the considered time series can be reconstructed in the 7M-dimensional phase space
by calculating the correlation exponent from the correlation integral (C(r)) as follows:
In this paper, we will employ an axiomatic definition for the phase space
B which is similar to those introduced by Hale and Kato .
In this paper, I argue that chaotic systems do, in fact, provide examples of irreducible neo-Aristotelian teleology in mechanics, but only if their behavior is considered in terms of changes to extended objects in a phase space
, with aspects that can be mapped to notions of form and matter.
In the specific system, acceleration comes as a result of the overlapping of wave-particle resonances of different order in phase space
, and therefore is of chaotic nature, contrary to the coherent acceleration achieved in inhomogeneous plasmas by adjusting the electron-cyclotron resonance layer .
So the phase space
reconstruction of the initial sample sequences X(t) is required.
Handfield calls individual points of phase space
"snapshots:" they are representations of ways a world might be at a single time.
To lower the sidelobes of radar signals based on chaotic map, Reference  suggested making use of the chaotic weak-structure property to produce chaotic map, based on this idea Multi-Segment Bernoulli (MSB) system was proposed; Reference  suggested utilizing high dimensional chaotic map with more complicated phase space
structure to generate chaotic frequency modulated (FM) radar signal; Reference  took advantage of Hyper Chaotic Logistic Phase Coded (HCLPC) signal along with Tikhonov regularization method to lower sidelobes.
The now familiar Lorenz Attractor, a figure of eight made of plots of weather events in phase space