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
