A strict amplitude lower bound for the van der Pol equation and extensions to symmetric Liénard systems

Changjian Liu, Ziwei Zhuang

We prove that the amplitude of the unique limit cycle of the van der Pol equation $\ddot{x}+\mu (x^2-1)\dot{x}+x=0$ is strictly greater than $2$ for every $\mu >0$. The proof combines or…