The Qualitative Analysis of Nonlinear Parameterised Systems Part I Nonlinear Systems Representation and Dynamical Systems Theory

The analysis of parameterised nonlinear models is considered and a new approach is introduced which provides a framework for the global analysis of both continuous and discrete time nonlinear systems. The paper is divided into two parts. Part I provides an overview of nonlinear system representations and dynamical systems theory. This forms the basis for the results in the second part. Part II introduces a numerically based analysis tool and demonstrates that this provides a flexible framework for the analysis of a diverse range of nonlinear model types. It is shown, by extending the numerical algorithm, that the approach provides a global perspective to the results that is difficult to obtain using analytical methods alone. Simple examples are used to illustrate how the method detects typical bifurcation phenomena. A nonlinear feedback system is analysed in order to show how the new approach provides both qualitative information and a global perspective over a defined region of the systems parameter space. The method proves to be a powerful tool when used to probe the nonlinear characteristic of a system.