............................................................................................................. (6.6.26)

Or, ....................................................................................(6.6.27)

Using a similar procedure of method of multiple scales, to eliminate the secular terms from Eq. (6.6.6) one can write

.......................................... ( 6.6.28 )

Using in Eq.(6.6.13) and separating the real and imaginary parts following reduced equations are obtained.

...............................................................................(6.6.29)

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(6.6.30)

Now to express the above equations in their autonomous form one may use the following transformation.

................................................................................................................(6.6.31)

.............................................................................................. (6.6.32)

.............................................................. (6.6.33)

........................................... (6.6.34)

For steady state one can write

.....................................................................................................(6.6.35)

.......................................................................(6.6.36)