Hello,

I have an non coupled non linear oscillator.

I notice that, if I try to plot for a time too big, my plot doesn't converge anymore and didn't keep an elliptic trajectory. In other words, the plot didn't stay in the limit cycle.

**Do you know why, if tmax is too big, the solution is no longer stable ? Do you have ideas so that I can keep a stable limit cycle even if I increase tmax ?**

My code is the following :

**r:=sqrt((x(t)/a)^2+(z(t)/b)^2);**

**eqx:=diff(x(t),t)=alpha*(1-r^2)*x(t)+w*a/b*z(t);**

**eqz:=diff(z(t),t)=beta*(1-r^2)*z(t)-w*b/a*x(t);**

**EqSys:=[eqx,eqz];**

**params := alpha=1, beta=1, a=0.4, b=0.2, w=1;**

**EqSys := eval([eqx,eqz], [params]);**

**xmax := 0.8; zmax := 0.4; **

**tmax := 400;**

**ic:=[x(0)=0.4, z(0)=0]; **

**DEplot(EqSys, [x(t),z(t)], t= 0..tmax, [ic],linecolor=black, thickness=1,x(t)=-xmax..xmax, z(t)=-zmax..zmax, scaling=constrained,arrows=none);**

Thanks a lot for your help.