Can any body suggest me a straightforward way with low computational cost, for obtaining LCO amplitude and frequency for multi-dimensional phase space?
You simply need to plot time series solutions instead of phase portraits. You can solve the differential equations to find the accurate period. In order to do this, you need packages such as Python, Maple, MATLAB and Mathematica. I have written Dynamical Systems books on all of these packages and you can download my programs for free over the Web.
an old but useful way is to use the Describing Function method. If I am not mistaken Dr. Ronilson Rocha has used this method with chaotic circuits and systems with good success.