Protected Chaos in a Topological Lattice

Area of Science:

• Non-linear dynamics
• Condensed matter physics
• Network science

Background:

• Chaotic behavior typically destabilizes periodic dynamics.
• Non-trivial topology is known for protecting linear systems.
• The interplay between chaos and topology in non-linear systems remains largely unexplored.

Purpose of the Study:

• To investigate the role of non-trivial topology in stabilizing chaotic dynamics.
• To demonstrate robust topological protection of chaos in non-linear oscillators.
• To explore the potential for designing resilient non-linear networks using topological principles.

Main Methods:

• Incorporating chaotic Chua's circuits into a topological Su-Schrieffer-Heeger (SSH) circuit.
• Analyzing dynamics across linear to deep non-linear regimes.
• Examining bulk and edge scroll dynamics for topological signatures.

Main Results:

• Non-trivial topology endures and protects chaotic dynamics within a topological lattice.
• Topological robustness persists in the parametric state of chaotic boundary oscillations.
• Distinctive correlations in bulk and edge dynamics reveal the topological origin of protected chaos.

Conclusions:

• Topologically protected chaos is achievable in periodically driven systems.
• This phenomenon offers new pathways for designing resilient and adaptable non-linear networks.
• The findings challenge the notion that chaos inherently erodes stability in topological systems.