Numerical Localization (visualization) of Attractors: Self-excited and Hidden Attractors
From a computational point of view, attractors can be naturally regarded as self-excited attractors or hidden attractors. Self-excited attractors can be localized numerically by standard computational procedures, in which after a transient sequence, a trajectory starting from a point on an unstable manifold in a small neighborhood of an unstable equilibrium reaches an attractor (like classical attractors in the Van der Pol, Belousov–Zhabotinsky, Lorenz, and many other dynamical systems). In contrast, the basin of attraction of a hidden attractor does not contain neighborhoods of equilibria, so the hidden attractor cannot be localized by standard computational procedures.
Read more about this topic: Attractor
Famous quotes containing the words numerical and/or hidden:
“There is a genius of a nation, which is not to be found in the numerical citizens, but which characterizes the society.”
—Ralph Waldo Emerson (1803–1882)
“Our courage breaks like an old tree in a black wind and dies,
But we have hidden in our hearts the flame out of the eyes
Of Cathleen, the daughter of Houlihan.”
—William Butler Yeats (1865–1939)