Marcotte Christopher D
Durham University, Department of Computer Science, Durham DH1 3LE, United Kingdom.
Phys Rev E. 2024 Dec;110(6-1):064210. doi: 10.1103/PhysRevE.110.064210.
We develop a linear theory for the prediction of excitation wave quenching-the construction of minimal perturbations which return stable excitations to quiescence-for localized pulse solutions in models of excitable media. The theory accounts for an additional equivariance compared to the homogeneous ignition problem, and thus requires a reconsideration of heuristics for choosing optimal reference states from their group representation. We compare predictions made with the linear theory to direct numerical simulations across a family of perturbations and assess their accuracy for several models with distinct stable excitation structures. We find that the theory achieves qualitative predictive power with only the effort of continuing a scalar root, 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.
我们针对可激发介质模型中的局域脉冲解，开发了一种用于预测激发波猝灭的线性理论——构建使稳定激发恢复到静止状态的最小扰动。与均匀点火问题相比，该理论考虑了额外的等变性，因此需要重新考虑从其群表示中选择最优参考状态的启发式方法。我们将线性理论所做的预测与一系列扰动下的直接数值模拟进行比较，并评估其在具有不同稳定激发结构的几个模型中的准确性。我们发现，该理论只需继续求解一个标量根，就能实现定性预测能力，并且在许多情况下能实现定量预测能力。最后，我们将我们的预测技术的计算成本与用于确定扩展可激发系统转变的其他数值方法进行比较。
