A dynamical system is a
System that
changes over time. The change can be continuous, i.e. a *flow*
of system states, or discrete, i.e. a cascade or *map*. In other
words, flow and map describe its
System
Dynamics.

Flows and maps are mathematically described by evolution functions, often the solutions of differential equations, that project points in a system’s State Space to other points in this space.

A stable state in the evolution of a system is called a steady state. Steady states are grouped into the system’s Attractors. A switch between attractors is also called a Phase Transition of the system.

Systems that have structure and hence are potentially Complex Systems are far from Thermal Equilibrium; their stable states are thus Non-equilibrium Steady States. When We are interested in systems that are, have been, or could be stable, we are interested in the attractors defined by these states.

## References

- Wikipedia: “Dynamical System”
- DeLanda (2002),
*Intensive Science and Virtual Philosophy* - Frigg, Berkovitz and Kronz (2020): “The Ergodic Hierarchy”
- Friston (2018): “A free energy principle for a particular physics”