Center Manifold and The Analysis of Nonlinear Systems
As the stability of the equilibrium correlates with the "stability" of its manifolds, the existence of a center manifold brings up the question about the dynamics on the center manifold. This is analyzed by the center manifold reduction, which, in combination with some system parameter μ, leads to the concepts of bifurcations.
Correspondingly, two web services currently undertake the necessary computer algebra to construct just the center manifold for a wide range of finite dimensional systems (provided they are in multinomial form).
- One web service constructs slow manifolds for systems which are linearly diagonalised, but which may be non-autonomous or stochastic.
- Another web service constructs center manifolds for systems with general linearisation, but only for autonomous systems.
Read more about this topic: Center Manifold
Famous quotes containing the words center, manifold, analysis and/or systems:
“Against the Word the unstilled world still whirled
About the center of the silent Word.”
—T.S. (Thomas Stearns)
“The Lord wrote it all down on the little slate
Of the baby tortoise.
Outward and visible indication of the plan within,
The complex, manifold involvedness of an individual creature”
—D.H. (David Herbert)
“Ask anyone committed to Marxist analysis how many angels on the head of a pin, and you will be asked in return to never mind the angels, tell me who controls the production of pins.”
—Joan Didion (b. 1934)
“Our little systems have their day;
They have their day and cease to be:
They are but broken lights of thee,
And thou, O Lord, art more than they.”
—Alfred Tennyson (1809–1892)