Source code for using computer algebra package Reduce to construct emergent models of complex dynamical systems.
InvariantManifold: provides a Reduce procedure to construct a specified invariant manifold for a specified system of ordinary differential equations or delay differential equations. The invariant manifold may be any of a centre manifold, a slow manifold, an un/stable manifold, a sub-centre manifold, a nonlinear normal form, any spectral submanifold, or indeed a normal form coordinate transform of the entire state space.
StoNormalForm: derive a stochastic/non-autonomous coordinate transformation that separates slow, stable and unstable modes in a system of SDEs or non-autonomous ODEs (or autonomous ODEs). This coordinate transform immediately gives the reduced model on the stochastic/non-autonomous slow manifold (and also other invariant manifolds), and the corresponding stochastic/non-autonomous isochrons which are so useful for projecting initial conditions and uncertainty quantification.
CentreManifold: replaced by InvariantManifold. This code used to provide the web service that does no longer exist but was at http://www.maths.adelaide.edu.au/anthony.roberts/gencm.php