When one considers a frequency dependent system, it can be reduced to an eigen value problem which depends on the eigen value itself, that is, a non-linear eigen value problem. It hosts an exceptional point as is a key phenomena of the non-Hermitian physics. We discuss it from a generic point of view in a recent paper, “Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues” by Tsuneya Yoshida, Takuma Isobe, and Yasuhiro Hatsugai publised in Phys. Rev. B 111, 064310 – Published 14 February, 2025. The simplest such an example is the Kapitza pendulum (See wikipedia). Also see arXiv:2407.20895.