stable manifold


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stable manifold

A mathematical term for the set of all points in phase space which are attracted to a fixed point or other invariant orbit in positive time.
References in periodicals archive ?
We will combine the nonlinear equations with information about the local dynamics to trace out the global stable manifold of the low-inflation steady state.
This approach will allow us to compute the global stable manifold of the low-inflation steady state.
If we begin with a point on that path, very close to the low-inflation steady state, and then iterate the nonlinear system backward, we can trace out the global dynamics associated with the saddlepath--the global stable manifold.
which indicates that the stable manifold of P is four-dimensional.
2] then one population will survive and the other population will become extinct; and if the initial population is on the stable manifold of [E.
31]; otherwise, if the initial population size is on the stable manifold of [E.
Biologically it means that if the initial population size of both x and y is on the stable manifold of [E.
Then F has the 1-dimensional local stable manifold [W.
and that this curve is a locally stable manifold of [?
a suspension" over a fraction of the stable manifold [W.
On the other hand, the past history of the deformation is determined by the (perturbed) stable manifold.
Since the two manifolds are invariant and the Poincare map preserves orientation, the enclosed region should be mapped another enclosed region infinitely many times along the unstable manifold, as t(or z) [right arrow] [infinity], or, along the stable manifold, as t (or z] [right arrow] [infinity].