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Target waves in the complex ginzburg-landau equation
1University of Maryland, Institute for Plasma Research, College Park, Maryland 20742, USA.
Summary
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.
- 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.
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