2. Nonlinear Systems

A brief overview of nonlinear systems is presented in this chapter. Nonlinear systems are inherently more complex to study than linear systems. Nonlinear systems possess many complex behaviors that are not observed in linear systems. Multiple equilibrium points, limit cycle, finite escape time, and chaos are illustrative of some of the complex behaviors of nonlinear systems. Global stability of a nonlinear system over its entire solution domain is difficult to analyze. Linearization can provide information on the local stability of a region about an equilibrium point. The phase plane analysis of a nonlinear system is related to that of its linearized systems because the local behaviors of the nonlinear system can be approximated by the behaviors of its linearized systems in the vicinity of the equilibrium points. Because nonlinear systems can have multiple equilibrium points, one important fact to note is that the trajectories of a nonlinear system can exhibit unpredictable behaviors.