The same chaotic time series can be embedded in different (or multiple) phase space
That's a region of phase space
that we haven't been able to look in before.
Henri Poincare, the 19th century French mathematician and theoretical physicist, developed a geometric approach called a homoclinic fixed point--a saddle point where stable and unstable trajectories intersect in phase space
38] first project the reconstructed phase space
on to any orthogonal two-dimensional plane (x(i), x(i + L)), where L = 0,.
WAVE PROPAGATION IN INHOMOGENEOUS MEDIA AS A CHAOTIC MIXING OF WAVEFRONT IN PHASE SPACE
Although, there is no specific definition for invariant manifold (positive), the behaviour of the immersed manifold along the trajectories in a phase space
will be measured.
The idea of the algorithm is if points are sufficiently close in a reconstructed phase space
, then they should remain close in the next.
Nonlinearity of the EEG and other types of biosignals has been studied by applying nonlinear analysis methods such as Detrended Fluctuation Analysis (DFA) , Poincare Plots , reconstruction of Local Phase Space
, segmentation of the EEG signal into stationary fragments , application of non-linear operators to the EEG time series .
The discrete-time multivariate modulated processes and functions he considers can depend not only on price but also on an additional stochastic index component with a general phase space
The team's detailed modeling, together with previous observations of peaks in electron phase space
density reported earlier this year by Geoff Reeves and colleagues in the journal Science, demonstrates the remarkable efficiency of natural wave acceleration in Earth's near-space environment and shows that radial diffusion was not responsible for the observed acceleration during this storm, Thorne said.
The temporal evolution of a system can be described by a multi-dimensional phase space
t] belongs to some abstract phase space
B, to be specified later, and [phi] [member of] B.