:yuck: I numerically integrate the following nonlinear oscillator: x''(t) + e (x'(t)^3) + x(t) = 0 , where e<<1 and what I get is a limit cycle. The energy derivative appears to be negative , which means that x(t) approaches zero while t approaches infinity. I also used the analytical method of two-timing, and the first asymptotic term x0(t) does approach zero for large t. ( The algorithm for the numerical integration is Runge-Kutta4. It's unlikely to have written it incorrectly.) So where am I wrong? Is it possible there is a limit cycle after all?