Identification of Continuous-Time Dynamical Systems: Neural Network Based Algorithms and Parallel Implementation

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.