Dynamical systems considered as ordering machines

When studying a nonlinear dynamical system, one is foremost interested in finding all the attractors which represent the long-term stable motions. The attractors could be equilibrium states, periodic motions, quasi-periodic motions, or strange attractors. All the states which are not associated with attractors are transient states. For each of the transient states one wishes to know which attractor the system will evolve to if it starts from that transient state, and how long it takes to go from that transient state to its final attractor. In addition, one is interested in locating the domains of attraction for each attractor and the boundary sets between the domains of attraction. This is the information one wishes to have, preferably all at once, when one is interested in the global behavior of a dynamical system. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.