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:
“Children can’t be a center of life and a reason for being. They can be a thousand things that are delightful, interesting, satisfying, but they can’t be a wellspring to live from. Or they shouldn’t be.”
—Doris Lessing (b. 1919)
“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)
“Whatever else American thinkers do, they psychologize, often brilliantly. The trouble is that psychology only takes us so far. The new interest in families has its merits, but it will have done us all a disservice if it turns us away from public issues to private matters. A vision of things that has no room for the inner life is bankrupt, but a psychology without social analysis or politics is both powerless and very lonely.”
—Joseph Featherstone (20th century)
“Before anything else, we need a new age of Enlightenment. Our present political systems must relinquish their claims on truth, justice and freedom and have to replace them with the search for truth, justice, freedom and reason.”
—Friedrich Dürrenmatt (1921–1990)