Phase space


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Related to Phase space: Liouville's theorem

Phase space

A graph which shows all possible states of a system. In phase space we plot the value of a variable against possible values of the other variables at the same time. If a system had three descriptive variables, we plot the phase space in three dimensions, with each variable taking one dimension.
References in periodicals archive ?
The same chaotic time series can be embedded in different (or multiple) phase space.
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,.
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) [5], Poincare Plots [6], reconstruction of Local Phase Space, segmentation of the EEG signal into stationary fragments [7], application of non-linear operators to the EEG time series [8].
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.