Some of the Limit Cycle Problems and Critical points for Planar Systems

Abstract

This study is an applied analytical one that helps in solving problems of the limit cycle and critical points for Planar systems. We introduced the classification of stable and unstable critical points of linear and nonlinear systems. The study found that the linear systems do not have a limit cycle. The study dealt with isolated limit cycle with its different patterns in an analytical and applied manner in the differential Planar systems of the second degree. The study investigated the problems related to the system limit cycle from Liénard type, and the researcher cited many examples and applications in this field. We discussed the problems of the limit cycle from the system other than Liénard and the method of converting it into the system from type of Liénard by applying some different techniques such as some nonlinear integrations, methods of comparison and some conversion techniques, and we supported this field with appropriate examples and applications. From these we concluded the application of some functions, equations and theories such as Dulac, Vander pol and Poincare, respectively. And thatsome of the systems do not have limit cycle, some of them have a single and stable limit cycle (Liénard), and some of them have many limit points