State Space

#concept12 mentions

A state space (or, which is roughly equivalent, phase space) is the set of all possible states of a Dynamical System; each state of the system corresponds to a unique point in the state space.

Describing a system in its state space means switching from a simple space (with 3 dimensions) and complex things (made out of N elements) to a complex space (3^N dimensions) and simple things (points in that space).

A system’s development over time, i.e. its System Dynamics, is equivalent to a trajectory in its state space. All possible trajectories in the space can be expressed as vectors; their aggregation is called the phase portrait of the state space.

The regions of the state space in which a system stays or to which it returns (i.e. in which it is stable) are the system’s Attractor regions.

An Attractor Landscape is the abstraction of a state space to what is relevant, i.e. interesting to us – attractors and possible trajectories between them.