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
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