论文标题
关于dirac $δ$脉冲的解释，相位振荡器的微分方程
On the interpretation of Dirac $δ$ pulses in differential equations for phase oscillators
论文作者
论文摘要
在本说明中，我们讨论了DIRAC $δ$在具有脉动输入的相位振荡器模型中的用法。许多作者在颂歌的右侧使用增量功能的产物和相位响应曲线，以描述此类系统中的不连续相动态。我们指出，该符号必须谨慎对待，因为它模棱两可。我们认为，大概大多数规范的解释在许多情况下不会导致预期的行为。
In this note we discuss the usage of the Dirac $δ$ function in models of phase oscillators with pulsatile inputs. Many authors use a product of the delta function and the phase response curve in the right hand side of an ODE to describe the discontinuous phase dynamics in such systems. We point out that this notation has to be treated with care as it is ambiguous. We argue that the presumably most canonical interpretation does not lead to the intended behaviour in many cases.
