What is phase space reconstruction?

What is phase space reconstruction?

Phase space reconstruction (PSR) is the foundation of nonlinear time series analysis that allows the reconstruction of complete system dynamics using a single time series [15]. Using this theorem, a single vector of observations representing a chaotic system can be regenerated into multidimensional vectors series.

Is phase space 6 dimensional?

The phase space of a particle is a six-dimensional space, three axes for momentum and three for position, so that each point of a particle’s phase space represents a complete state of the particle, and the entire phase space represents all possible states of the particle. …

What is phase space dimensional?

The phase space of a two-dimensional system is called a phase plane, which occurs in classical mechanics for a single particle moving in one dimension, and where the two variables are position and velocity. As the system evolves, its state follows one of the lines (trajectories) on the phase diagram.

What is a phase space diagram?

A phase-space plot is a parametric graph of the velocity v(t) plotted as a function of the displacement x(t), with the changing variable being time. Phase-space plots are very useful for analyzing more complicated oscillations, especially oscillation that tends towards chaos.

How is the embedding dimension of phase space reconstruction estimated?

For reconstruction, the time delay is set to be the first local minimum of AMI. where, N is the length of the time series and Τ = 1:MaxLag. The embedding dimension for phase space reconstruction is estimated using False Nearest Neighbor (FNN) algorithm. where, is the distance metric.

How are two dimensional systems represented in phase space?

Phase space. In a phase space, every degree of freedom or parameter of the system is represented as an axis of a multidimensional space; a one-dimensional system is called a phase line, while a two-dimensional system is called a phase plane. For every possible state of the system, or allowed combination of values of the system’s parameters,…

What is phase space reconstruction ( PSR ) used for?

Phase space reconstruction (PSR) is one of the widely used methods for chaotic time series analysis. The APM mass concentrations are an outcome of complex anthropogenic contributors evolving with time, which may operate on multiple time scales.

When to use phasespacereconstruction as a first step?

Reconstructing the phase space is useful when limited data is available, or when the phase space dimension and lag is unknown. The nonlinear features approximateEntropy, correlationDimension, and lyapunovExponent use phaseSpaceReconstruction as the first step of the computation.