On a Dynamic Wavelet Network and Its Modeling Application

This study presents a nonlinear dynamical system modeling with dynamic wavelet networks (DWNs). Wavelet is widely used in processing of signals and data. It has been also shown that wavelet can be effectively used in nonlinear system modeling. For this, dynamic wavelet networks (DWNs) structure based on Hoppfield networks has been developed. DWN has a lag dynamic, non orthogonal mother wavelets as activation function and interconnection weights. Network weights are adjusted based on supervised training. With fast training algorithms (quasi-Newton methods), wavelet networks are trained. In this paper, Mexican Hat wavelet. First, a phase-portraits based example is given. For this, it has been shown that DWN has chaos properties. The last, a dynamical system with discrete-event is modeled using DWN. There is a localization property at discrete-event instant for time-frequency in this example.