Model reduction via parametrized locally invariant manifolds: Some examples

A method for model reduction in non-linear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint, the method has the potential of serving as a subgrid modeling tool. From the physical standpoint, it provides a model for interpreting and describing history dependence in coarse-grained response of an autonomous system.