On uniqueness of limit cycle for the equation ¨x + f (x)φ( ˙x) ˙x +g(x) = 0

In this paper, we use the theory of generalized rotated fields to prove a theorem of the uniqueness of limit cycle for the generalized Liénard system. The damping terms of this system are dependent on ˙x. Our result extends a famous Zhang–Zhifen’s theorem on the uniqueness problem of limit cycle, which is contributed the Liénard systems whose damping terms are independent of ˙x.  2003 Elsevier Inc. All rights reserved