<p>Contact defects are time-periodic patterns that resemble spatially homogeneous oscillations in the far field and exhibit a phase defect in the core region. In prior work, we showed that contact defects in reaction–diffusion systems on the real line persist under truncation to large bounded intervals. Here, we investigate spectral stability of contact defects under domain truncation. We prove that contact defects on large bounded domains (i) inherit spectral stability from the real line under periodic boundary conditions and (ii) become spectrally unstable under Neumann boundary conditions. In particular, interacting contact defects on large domains will attract or repel each other, validating the dynamical behavior of phase defects that arise naturally as line defects in period-doubled planar spiral waves.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Spectral Stability of Contact Defects on Large Bounded Domains

  • Milen Ivanov,
  • Björn Sandstede

摘要

Contact defects are time-periodic patterns that resemble spatially homogeneous oscillations in the far field and exhibit a phase defect in the core region. In prior work, we showed that contact defects in reaction–diffusion systems on the real line persist under truncation to large bounded intervals. Here, we investigate spectral stability of contact defects under domain truncation. We prove that contact defects on large bounded domains (i) inherit spectral stability from the real line under periodic boundary conditions and (ii) become spectrally unstable under Neumann boundary conditions. In particular, interacting contact defects on large domains will attract or repel each other, validating the dynamical behavior of phase defects that arise naturally as line defects in period-doubled planar spiral waves.