:yuck: I numerically integrate the following nonlinear oscillator:(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# A question about a nonlinear oscillator

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