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Target waves in the complex ginzburg-landau equation

Hendrey1, Nam, Guzdar

  • 1University of Maryland, Institute for Plasma Research, College Park, Maryland 20742, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|January 4, 2001
PubMed
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Localized inhomogeneity in the complex Ginzburg-Landau equation creates stationary and breathing target waves. Breathing waves exhibit quasiperiodic temporal modulation near the target center.

Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Complex systems

Background:

  • The complex Ginzburg-Landau equation models various phenomena, including pattern formation.
  • Understanding wave propagation and pattern dynamics is crucial in nonlinear systems.
  • Spatially localized perturbations can significantly alter system behavior.

Purpose of the Study:

  • To investigate the effects of a spatially localized inhomogeneity on the two-dimensional complex Ginzburg-Landau equation.
  • To characterize the resulting target wave patterns and their dynamics.
  • To explore the transition between different wave patterns and their interactions.

Main Methods:

  • Numerical simulations of the two-dimensional complex Ginzburg-Landau equation.
  • Introduction of a spatially localized inhomogeneity as a perturbation.

Related Experiment Videos

  • Analysis of field variables and temporal modulations near the target center.
  • Investigation of transitions and competition between different wave types.

    • Main Results:

    • Two types of target wave patterns were observed: stationary and breathing.
    • Breathing target waves exhibit quasiperiodic temporal modulation near the center.
    • A transition between stationary and breathing targets with hysteresis was identified.
    • Competition between target waves and spiral waves was discussed.

    Conclusions:

    • Localized inhomogeneities can induce complex spatio-temporal dynamics in the complex Ginzburg-Landau equation.
    • The study reveals distinct behaviors of stationary and breathing target waves.
    • Hysteresis in pattern transitions and wave competition are significant findings.