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Nonlinear case, expanding about an equilibrium point. Need to know the nonlinear vector field along the center manifold.
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Center Manifold Theory - Computing Center Manifolds
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- 1 ► Jump to center manifold theory computations:
- 2 Center Manifold Theory introduction
- 3 Motivation from linear vector fields with block diagonal matrix D=diag{A,B} where A has only eigenvalues of zero real part and B is a matrix having only eigenvalues of negative real part. We need to…
- 4 Nonlinear case, expanding about an equilibrium point. Need to know the nonlinear vector field along the center manifold.
- 5 Center manifold theory computation
- 6 Approximate the center manifold locally as a function and do a Taylor series expansion to obtain it
- 7 Vector field on the center manifold
- 8 the tangency condition, main computational 'workhouse'
- 9 2D example: two-dimensional system where stability of the origin is not obvious
- 10 Why not do a tangent space (Galerkin) approximation for center manifold dynamics?
- 11 3D example with 2D center manifold
