We develop linear theory for the prediction of excitation wave quenching--the construction of minimal perturbations which return stable excitations to quiescence--for localized pulse solutions of models of excitable media. The theory requires accounting for an additional degree of freedom in the formulation of the linear theory, and a reconsideration of heuristics for choosing optimal reference states from their group representation. We compare the predictions made with the linear theory to direct numerical simulations across a family of perturbations and assess the accuracy of predictions for models with distinct stable excitation structures. We find that the theory achieves qualitative predictive power with only the effort of distinguishing a root from the asymptotic case, and achieves quantitative predictive power in many circumstances. Finally, we compare the computational cost of our prediction technique to other numerical methods for the determination of transitions in extended excitable systems.

翻译：我们发展了线性理论，用于预测激发波淬灭——即构建使稳定激发回归静息状态的最小扰动——针对可兴奋介质模型中的局域脉冲解。该理论要求在构建线性理论时考虑额外的自由度，并重新审视从群表示中选择最优参考状态的启发式方法。我们将线性理论的预测与一系列扰动下的直接数值模拟进行比较，评估了具有不同稳定激发结构模型的预测准确性。研究发现，只需区分根与渐近情形，该理论即可获得定性预测能力，并在多种情况下实现定量预测。最后，我们将预测技术的计算成本与用于确定扩展可兴奋系统转变的其他数值方法进行了比较。