Limit Cycle Analysis of 3-D Nonlinear systems

Considering Limit Cycles as one of the limits of Lienard equation, an analyis analogous to centre manifold analysis has been done for a $3-D$ nonlinear system exhibiting Limit Cycle. A rigorous study on radius of the Limit Cycle orbit has been done by considering $\lambda-\omega$ equations for the particular system and subsequently converting the system equations from cartesian to polar form. It has been shown through an analysis analogous to Centre Manifold Analysis and reduction of the system dynamics on a lower dimensional space, the Limit cycle radius undergoes an increment change. One example is provided to support the theoretical predictions.