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<p>The Lengyel–Epstein mathematical model for the CIMA chemical reaction is studied. The concentrations depend on time and a single spatial coordinate, so that one-dimensional patterns in space are possible. A linearized solution for the spatial patterns is presented, and the question of pattern selection is addressed. Nonlinear patterns are discussed and compared against the predictions of linearized theory. It is found that spatially-homogeneous time-dependent oscillations exist, born from Hopf bifurcations. In addition, Turing bifurcations also occur, and give rise to steady-state patterns. Furthermore, these steady patterns can undergo further bifurcation at large amplitude. These one-dimensional stationary patterns are quasi-stable, in the sense that they may persist for some time, but ultimately, they collapse onto the spatially-homogeneous limit-cycle solutions.</p>

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One-dimensional spatio-temporal patterns in the CIMA reaction

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Reuben Allen,
  • Heath Dimsey,
  • Michael Brideson,
  • Lawrence Forbes

摘要

The Lengyel–Epstein mathematical model for the CIMA chemical reaction is studied. The concentrations depend on time and a single spatial coordinate, so that one-dimensional patterns in space are possible. A linearized solution for the spatial patterns is presented, and the question of pattern selection is addressed. Nonlinear patterns are discussed and compared against the predictions of linearized theory. It is found that spatially-homogeneous time-dependent oscillations exist, born from Hopf bifurcations. In addition, Turing bifurcations also occur, and give rise to steady-state patterns. Furthermore, these steady patterns can undergo further bifurcation at large amplitude. These one-dimensional stationary patterns are quasi-stable, in the sense that they may persist for some time, but ultimately, they collapse onto the spatially-homogeneous limit-cycle solutions.