Stability analysis of singular patterns in the 1 D Gray-Scott model : a matched asymptotics approach

  title={Stability analysis of singular patterns in the 1 D Gray-Scott model : a matched asymptotics approach},
  author={Arjen Doelman and Robert A. Gardner and Tasso J. Kaper},
In this work, we analyze the linear stability of singular homoclinic stationary solutions and spatially periodic stationary solutions in the one-dimensional Gray-Scott model. This stability analysis has several implications for understanding the recently discovered phenomena of self-replicating pulses. For each solution constructed in A. Doelman et al. [Nonlinearity 10 (1997) 523-563], we analytically find a large open region in the space of the two scaled parameters in which it is stable… CONTINUE READING
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