Perturbations of circuit evolution matrices with Jordan blocks

In our prior studies, we synthesized special circuits with evolution matrices featuring degenerate eigenfrequencies and nontrivial Jordan blocks. The degeneracy of this type is sometimes referred to as exceptional point (EPD). Our focus here on the simplest EPDs that are composed only two LC-loops coupled by a gyrator. These circuits, when near an EPD state, can be used for enhanced sensitivity applications. With in mind, develop comprehensive perturbation theory these simple EPD. Using theory, propose approach sensing, allowing one benefit from proximity hand providing stable operation other hand. We also address broader scope problems related perturbations blocks their numerical treatment allow us effectively detect