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.
References
- Abraham & Shaw (1995): Dynamics: The Geometry of Behavior
- DeLanda (2002): Intensive Science and Virtual Philosophy
- Terman & Izhikevich (2008): “State space“