  The role of nonlinearity on topology has been investigated extensively in
Hermitian systems, while nonlinearity has only been used as a tuning knob in a
PT symmetric non-Hermitian system. Here, in our work, we show that nonlinearity
plays a crucial role in forming topological singularities of non-Hermitian
systems. We provide a simple and intuitive example by demonstrating with both
theory and circuit experiments an exceptional nexus (EX), a higher-order
exceptional point with a hybrid topological invariant (HTI), within only two
coupled resonators with the aid of nonlinear gain. Phase rigidities are
constructed to confirm the HTI in our nonlinear system, and the anisotropic
critical behavior of the eigenspectra is verified with experiments. Our
findings lead to advances in the fundamental understanding of the peculiar
topology of nonlinear non-Hermitian systems, possibly opening new avenues for
applications.
