Dynamical systems

A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space.

At any given time a dynamical system has a state given by a set of real numbers (a vector) that can be represented by a point in an appropriate state space (a geometrical manifold). Small changes in the state of the system create small changes in the numbers. 

The Lornenz system is often an example of dynamic system that is also chaotic under some initial conditions. image: wikipedia

The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state. The rule is deterministic; in other words, for a given time interval only one future state follows from the current state.

source: http://en.wikipedia.org/wiki/Dynamical_systems

Commentary:

There is quite a difference in the definition on wikipedia and on wolfram ( a mathematics expert organisation) . The main issue is that the wikipedia definition does not explicitly discuss chaos theory in the first instance. i.e.  that a dynamical system is sensitive to initial conditions which may create large unstable situations.