Phase Diagrams and Stability

Abstract

In most realistic models of scientific and engineering systems one is confronted with the necessity to analyze and solve systems of nonlinear differential equations. However, since the search for exact analytic solutions of such systems is, in most instances hopeless, it is natural to inquire in retrospect what is the most crucial information that has to be extracted from these equations. One discovers then that many such systems have transient states which are time dependent and equilibrium states which are time independent states. The equilibrium states are usually the most significant from a practical point of view and their stability against small perturbations and/or small changes in the system parameters is a central problem in the design and analysis of these systems.