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Topologically protected edge oscillations in nonlinear dynamical units.

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Topological protection ensures robust dynamics in classical oscillators. This study demonstrates edge-localized oscillations in a 2D grid, resilient to noise and defects, via a bulk-boundary correspondence.

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Area of Science:

  • Classical physics
  • Condensed matter physics
  • Nonlinear dynamics
  • Topological physics

Background:

  • Topological protection enhances dynamic robustness in quantum and classical systems.
  • Its role in classical oscillatory systems remains less explored.
  • Oscillator models with potential biochemical applications are considered.

Purpose of the Study:

  • Investigate topological protection in classical oscillatory systems.
  • Explore edge-localized oscillations and their robustness.
  • Analyze the underlying mechanisms using topological characteristics.

Main Methods:

  • Utilized prototypical oscillator models on a 2D grid with directed, alternating couplings.
  • Inspired coupling geometry from condensed matter physics models with nontrivial topology.
  • Calculated Zak phases to explain robustness of edge oscillations.
  • Derived an effective non-Hermitian Hamiltonian.

Main Results:

  • Achieved edge-localized oscillations and oscillation-death states in the bulk, forming a frequency-chimera-like state.
  • Demonstrated resilience of these patterns to parameter mismatches, noise, and defects.
  • Confirmed a bulk-boundary correspondence for edge oscillations, even with a non-Hermitian Hamiltonian.

Conclusions:

  • Topological protection can stabilize dynamics in classical oscillatory systems.
  • A bulk-boundary correspondence governs edge localization in this non-Hermitian system.
  • System parameters allow control over oscillatory and oscillation-death regions.