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Phase-space structure of two-dimensional excitable localized structures.

Damià Gomila1, Adrian Jacobo, Manuel A Matías

  • 1Unidad de Física Interdisciplinar, Instituto Mediterráneo de Estudios Avanzados, IMEDEA (CSIC-UIB), E-07122 Palma de Mallorca, Spain. damia@imedea.uib.es

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This summary is machine-generated.

Researchers detailed a bifurcation route to excitability in a nonlinear Kerr cavity. This emergent property arises from spatial dynamics, not local behavior, via a saddle-loop bifurcation.

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Area of Science:

  • Nonlinear optics
  • Dynamical systems theory
  • Cavity quantum electrodynamics

Background:

  • Dissipative nonlinear Kerr cavities with homogeneous pumping exhibit complex dynamics.
  • Localized structures play a key role in mediating transitions to different dynamical regimes.
  • Understanding the underlying bifurcations is crucial for controlling system behavior.

Purpose of the Study:

  • To characterize the bifurcation route leading to an excitable regime in a dissipative nonlinear Kerr cavity.
  • To elucidate the mechanism of reduction from an infinite-dimensional system to a planar dynamical system.
  • To demonstrate how excitability emerges as a spatial, rather than local, property.

Main Methods:

  • Detailed characterization of the bifurcation process.
  • Analysis using a planar dynamical system model.
  • Study of the reduction mechanism from an infinite-dimensional system.
  • Investigation of excitability under perturbations.

Main Results:

  • A saddle-loop bifurcation, where a limit cycle becomes a homoclinic orbit of a saddle point, is identified as the key route to excitability.
  • The transition to excitability is understood through a simplified planar dynamical system.
  • Excitability is shown to be an emergent property arising from spatial dependence.
  • The system does not exhibit local excitable behavior.

Conclusions:

  • The study provides a comprehensive understanding of the bifurcation leading to excitability in this nonlinear system.
  • The reduction to a planar dynamical system effectively captures the essential dynamics.
  • Excitability emerges from spatial interactions, highlighting the importance of localized structures.