Singularity structure analysis for nonlinear dynamic systems

The aim of this work is to develop an explicit system model which can characterize the system behavior in both the linear and nonlinear range. Fractal concepts and system theory are applied to develop the system model and the analytical methodology necessary to study the nonlinear behavior. The singularity structure model, which is a rational function with densely distributed singularities following a geometric sequence in the S-plane, has been developed for the analysis of relaxation processes in the linear range. The perturbation-dependent singularity structure is then used to model the nonlinear system in the time and frequency domain. An extended convolution method is proposed for analyzing the nonlinear behavior using the proposed system model. The physical system studied in this work is the electrode-electrolyte interface, and a high-precision measurement instrument has been used for observation. computational software has been developed to generate the simulated data. Both the model and the analysis method have been tested using experimental data collected in the linear and nonlinear ranges