Heterogeneity selected target waves and their competition: Outgoing or ingoing?

Traveling direction (outgoing or ingoing) of target waves sustained by a localized inhomogeneity and their competition rules in the complex Ginzburg–Landau equation (CGLE) are studied. We show that even a local positive (negative) frequency shift is capable of creating ingoing (outgoing) target waves. A novel transition between ingoing and outgoing target waves, as we find, can be switched by the size of the inhomogeneity. The competition rules for wave patterns (e.g., target waves) are also studied systematically. All the numerical findings are found to be in perfect agreement with the theoretical criteria that are derived based on the fundamental conceptions (e.g., group velocity, phase velocity).