On the interpretation of Dirac $\delta$ pulses in differential equations for phase oscillators
Chaotic Dynamics
2021-03-17 v2 Dynamical Systems
Abstract
In this note we discuss the usage of the Dirac 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.
Keywords
Cite
@article{arxiv.2012.01836,
title = {On the interpretation of Dirac $\delta$ pulses in differential equations for phase oscillators},
author = {Vladimir Klinshov and Leonhard Lücken},
journal= {arXiv preprint arXiv:2012.01836},
year = {2021}
}
Comments
a serious flaw in the paper