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：我们发展了用于预测激发波淬灭的线性理论——即构建使稳定激发回归静息状态的最小扰动——针对可激介质模型的局域脉冲解。该理论需要在线性理论框架中考虑一个额外的自由度，并重新审视从群表示中选择最优参考态的启发式方法。我们将该线性理论的预测结果与一族扰动下的直接数值模拟进行比较，并评估了该理论在不同稳定激发结构模型中的预测精度。研究发现，该理论仅需区分根源情形与渐进情形即可获得定性预测能力，并在多数情况下具备定量预测能力。最后，我们将本预测方法的计算成本与其他确定扩展可激系统中跃迁的数值方法进行了比较。