Raj,
a (stable) limit cycle is a kind of oscillation. An important example is an oscillation of a recursive digital filter in fixed-point arithmetic stimulated and sustained by the rounding error.

Which context interests you?
- B O E

Hi Raja,
This is more or less what I remember...
Typically in non-linear systems, the solutions to differential equations representing such systems have singularities around which the trajectory of such solution (in the plane defined by the state variables) cycle around such point.
As boe suggested they represent oscillations conditions that can be reached depending on the initial conditions of your non-linear system: a typical limit cycle is the switching of a buck converter when analyzed as a non-linear system, or idle tones on a sigma delta converter when also analyzed as non-linear feedback system.

Best
Tosei

Raja - The idle tones in a delta sigma modulator can be thought of as limit cycles, although I'm not sure if they are the same thing as what you are researching. See page 41-45 of Schreier/Temes's book.

rg