  Time-delay mappings constructed using neural networks have proven successful
in performing nonlinear system identification; however, because of their
discrete nature, their use in bifurcation analysis of continuous-time systems
is limited. This shortcoming can be avoided by embedding the neural networks in
a training algorithm that mimics a numerical integrator. Both explicit and
implicit integrators can be used. The former case is based on repeated
evaluations of the network in a feedforward implementation; the latter relies
on a recurrent network implementation. Here the algorithms and their
implementation on parallel machines (SIMD and MIMD architectures) are
discussed.
