Systems have things with features. System models {phase space, system}| can use abstract-space nodes to represent things and can use dimensions to represent features or factors. Nodes can be system states. Similar states are near each other. Low-dimension systems have less information about nodes, because nodes have fewer factors. High-dimension systems have more node information. With more dimensions, phase-space-model predictability declines, information flows increase, and mixing increases.
Phase space can represent variable values over time {plotting}|. First dimension is for value at time t, second dimension is for value at time t + 1, and so on. For simple processes, phase spaces can have characteristic shapes.
Phase-space points or trajectories can project onto two-dimensional surfaces or three-dimensional solids {projection, phase space}. New dimensions are phase-space-dimension composites.
Phase spaces can have cross-sections {return map} {Poincaré map} {Poincaré section} of fewer dimensions. Phase-space points, nodes, and trajectories can project onto cross-section.
Phase space can have only several widely separated nodes {sparse population coding}. Nodes can represent complex states. States are not similar to other states. Sparse population coding can be for pattern or object recognition [Kanerva, 1988].
3-Computer Science-System Analysis
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Date Modified: 2022.0225