ABSTRACT
In this chapter, the concepts for solving algebraic and differential equations are used for simulation and analysis of nonlinear systems. The chapter focuses on methods to analyze the dynamic behavior of nonlinear systems, and on specific simulation examples of relevance to process engineers. It considers a nonlinear analysis of the chemostat and an investigation of bifurcation behavior. The linear stability analysis provides a local dynamical behavior of the system in the vicinity of the steady state. The salient features of transcritical bifurcation are that both the solutions continue to exist numerically on either side of the bifurcation point; however, there is an exchange of stability in one or both types of solutions. Phase-plane analysis is very useful to get a global picture of the system behavior. The documentation for MATLAB ordinary differential equation (ODE) solvers describes a van der Pol oscillator. It is a standard example of nonlinear oscillating systems.
