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A (dissipative) dynamical system can be described by a set
of ordinary differential equations:
and when time is not continuous but assumes only discrete values
by difference equations (maps):
For dissipative systems, phase-space volumes are contracted by the
time evolution. The trajectory (orbit) of such a system typically settles on
a subset of , called an attractor [Eckmann and Ruelle, 1985].
For example, the attractor of a damped pendulum is a fixed point,
while the attractor of a periodically forced
pendulum is a limit cycle.
On a strange attractor, trajectories wander in an
apparently erratic manner and they are highly sensitive to initial
conditions. For a zoo of strange attractors, see Ref. [Holden and Muhamad, 1986].