狄拉克$δ$脉冲在相位振荡器微分方程中的解释
On the interpretation of Dirac $δ$ pulses in differential equations for phase oscillators
摘要：
本文讨论了Dirac $δ$函数在具有脉冲输入的相位振荡器模型中的应用。许多作者用δ函数和常微分方程右侧的相响应曲线的乘积来描述这类系统中的不连续相动力学。我们指出，这个符号必须小心对待，因为它是模棱两可的。我们认为，在许多情况下，可能最规范的解释并不导致预期的行为。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
