奇异摄动相位响应曲线
Singularly perturbed phase response curves
AI总结：
本文提出基于奇异摄动的几何方法，用于近似弛豫振荡器等时线并预测有限相位响应曲线，克服无穷小方法在奇异极限附近的局限，并在FitzHugh-Nagumo模型上验证了半解析公式的有效性。
摘要：
本文提出一种基于奇异摄动的新颖几何方法，用于近似弛豫振荡器的等时线，并预测其（有限）相位响应曲线的定性形状。该方法补充了针对弛豫振荡器的无穷小相位响应曲线方法，并克服了后者在奇异极限附近的局限性。我们通过推导一般平面弛豫振荡器对脉冲和有限时长方波脉冲的（有限）相位响应曲线的半解析公式来展示该方法的效力，并在FitzHugh-Nagumo模型上数值验证了其优良性。
英文摘要：
In this paper we propose a novel geometric method, based on singular perturbations, to approximate isochrones of relaxation oscillators and predict the qualitative shape of their (finite) phase response curve. This approach complements the infinitesimal phase response curve approach to relaxation oscillators and overcomes its limitations near the singular limit. We illustrate the power of the methodology by deriving semi-analytic formula for the (finite) phase response curve of generic planar relaxation oscillators to impulses and square pulses of finite duration and verify its goodness numerically on the FitzHugh-Nagumo model.
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