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”