Adaptive series-parallel identification of dynamical systems with uncertain bifurcations and chaos

Identifying a real-world dynamical system with uncertain transitions among bifurcations and chaos is a first step in applying the celebrated chaos theory to a real world phenomenon with such transitions. This paper describes a systematical method of performing such a first step using measurement data alone. The adaptive identifiers used are adaptive neural networks (i.e. NNs with long- and short-term memories), whose effectiveness for adaptive system identification has been reported in the recent LJCNNs. Numerical results are reported of applying such NNs to adaptive series-parallel identification of four well-known dynamical systems with uncertain bifurcations and chaos, namely a predator-prey model, Henon system, blood cell population model, and Lorenz system, which are 2-D, 2-D, 1-D and 3-D respectively.