Constraint Cycles in Quadratic Framework with Their Properties

Abstract

In this study, an analysis is performed to study the reality and individuality of the limit cycle for a quadratic system. An algorithm is narrated for finding focal basis. These evaluations are then utilized to compute the small-amplitude limit cycle. The same approach is applied to the quadratic system and examples are formulated constructed for the small-amplitude limit cycle. For this quadratic system in the plane of two autonomous differential equations is considered, examples are also constructed by utilizing the technique of bifurcation of limit cycle & Poincare Bendixon theorem. Besides the number and distribution of limit cycle in the system are also discussed.