  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.
