6 \(x''(t)+f(x)x'(t)+x(t)=0\) and periodic solutions

This shows dependence of having perodic solutions for \(x''(t)+f(x)x'(t)+x(t)=0\) where \(f(x)=x^2+x+a\) on the value of \(a\). This simulations shows the solution and the phase space as \(a\) changes from \(-2\) to \(1\). A specific orbit with I.C. \(x(0)=1,x'(0)=0\) is highlighted in red.

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The program is written using Mathematica. Here is the notebook

Source code