Regensburg 2025 – scientific programme

Parts | Days | Selection | Search | Updates | Downloads | Help

DY: Fachverband Dynamik und Statistische Physik

DY 34: Nonlinear Dynamics, Synchronization, and Chaos

DY 34.6: Talk

Thursday, March 20, 2025, 12:45–13:00, H43

Designing Robust Edge Oscillations with Topological Protection in Nonlinear Coupled Systems — •Sayantan Nag Chowdhury and Hildegard Meyer-Ortmanns — School of Science, Constructor University, 28759 Bremen, Germany

Topological protection, a powerful concept in physics, ensures robust states across quantum and classical systems. While topological insulators exemplify its applications in quantum systems with electric currents protected along the edges, an example from classical physics is provided by topoelectrical circuits with stable signal transduction. However, the role of topological protection in the context of classical oscillatory systems has been much less explored. Our study applies tools from band theory of condensed matter physics to systems with nonlinear dynamics to achieve robust edge oscillations. This means that oscillations are restricted to the edge of a two-dimensional grid, while those in the bulk settle into near-steady-state dynamics. This pattern is resilient to parameter mismatches, structural defects, and blockages. By calculating the Zak phase as topological characteristic for this phenomenon, we explain edge-localized oscillations through bulk-boundary correspondence. We further analyze the collective behavior by examining the limiting case of weak coupling strength in our directed network, which alternates between strong and weak values. We validate our findings for different prototypical oscillator models with possible applications in biochemical systems. Our findings establish a robust design for controlling the state of oscillation of units that are attached to a spatial grid.

Keywords: Nonlinear dynamics; Edge-localized oscillations; Spatially structured networks; Topological protection; Bulk-boundary correspondence