Topological Metamorphosis and Bifurcation Trajectories of Non-Hermitian Singularities

Numerous studies on non-Hermitian physics have remained confined to isolated exceptional points (EPs) and relied on complex parameters to analyze their physical characteristics [1–20]. Because manipulating such complex variables poses significant engineering constraints in real-world applications, recent efforts have focused on shifting the operational framework towards pure real-parameter spaces or continuous regimes [21–23]. To overcome these limitations, a recent study investigated a purely real-parameter passive system, successfully elucidating an L-surface where innumerable loci of EPs cluster together [24]. To demonstrate that this phenomenon is not an accidental occurrence but a generalized physical trait, we applied this framework to a three-degree-of-freedom semi-definite damped system, thereby establishing its systemic universality. Importantly, we discovered that the inertia of this bare primary mass acts as a critical topological switch: varying its scale governs whether the system coalesces into the L-surface or branches into alternative physical regimes. By treating this ungrounded mass as a key scaling parameter, we define the exact boundaries that map these diverse topological states. Given its high configurability, this framework opens up new avenues for multi-functional wave guiding, adaptive energy harvesting, and highly sensitive topological sensors, expanding the practical utility of non-Hermitian systems previously explored [24].