Global bifurcations and basin geometry of the nonlinear non-Hermitian skin effect

• URL: http://arxiv.org/abs/2602.17439v1
• Date: Thu, 19 Feb 2026 15:07:50 GMT
• Title: Global bifurcations and basin geometry of the nonlinear non-Hermitian skin effect
• Authors: Heng Lin, Yunyao Qi, Gui-Lu Long,
• Abstract summary: We study a continuum Hatano-Nelson-Nelson model with a saturating nonlinear nonreciprocity.<n>We analyze its stationary states via the associated phase-space flow.
• Score: 0.574717310498622
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study a continuum Hatano--Nelson model with a saturating nonlinear nonreciprocity and analyze its stationary states via the associated phase-space flow. We uncover a global scenario controlled by a subcritical Hopf bifurcation and a saddle-node of limit cycles, which together generate a finite coexistence window. In this window, skin modes and extended states are both stable at a fixed energy $E$, separated by a nonlinear basin separatrix in phase space rather than a spectral (mobility-edge) mechanism in a linear system. An averaged amplitude equation yields closed-form predictions for the limit-cycle branches and the SNLC threshold. Building on the basin geometry, we introduce a basin-fraction order parameter that exhibits a first-order-like jump at SNLC. Intriguing physical phenomena in the coexistence window are also revealed, such as separatrix-induced long-lived spatial transients and hysteresis. Overall, our findings highlight that, beyond linear spectral concepts, global attractor-basin geometry provides a powerful and complementary lens for understanding stationary states in nonlinear non-Hermitian systems.

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