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An external cavity laser with strong grating-filtered feedback to an antireflection-coated facet is studied with a time-domain integral equation for the electric field, which reproduces the modes of the oscillation condition as steady-state solutions. For each mode, the stability and spectral behavior is determined by analysis of the location of side modes in the complex frequency plane. The complex frequency diagrams are shown to be a useful tool to determine the self-stabilization effect of mode coupling and its dependence on laser parameters and external cavity design. The model is used to simulate the large signal time evolution after start from unstable modes.