Topological and chaotic dynamics are often considered incompatible, with one expected to dominate or disrupt the other. This work reveals that topological localization can persist even under strong chaotic dynamics and, counter-intuitively, protect chaotic behavior. The findings challenge the conventional view that chaos erodes regular oscillations, showing instead that it can be protected by topology in non-linear dynamical lattices.
Abstract
The erratic nature of chaotic behavior is thought to erode the stability of periodic behavior, including topological oscillations. However, it is discovered that in the presence of chaos, non-trivial topology not only endures but also provides robust protection to chaotic dynamics within a topological lattice hosting non-linear oscillators. Despite the difficulty in defining topological invariants in non-linear settings, non-trivial topological robustness still persists in the parametric state of chaotic boundary oscillations. This interplay between chaos and topology is demonstrated by incorporating chaotic Chua’s circuits into a topological Su-Schrieffer-Heeger (SSH) circuit. By extrapolating from the linear limit to deep into the non-linear regime, it is found that distinctive correlations in the bulk and edge scroll dynamics effectively capture the topological origin of the protected chaos. The findings suggest that topologically protected chaos can be robustly achieved across a broad spectrum of periodically driven systems, thereby offering new avenues for the design of resilient and adaptable non-linear networks.
Advanced Science, EarlyView. Read More
