On the interpretation of Dirac $\delta$ pulses in differential equations for phase oscillators

Autor:	Klinshov, Vladimir, Lücken, Leonhard
Rok vydání:	2020
Předmět:	Nonlinear Sciences - Chaotic Dynamics Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
DOI:	10.1063/5.0040995
Popis:	In this note we discuss the usage of the Dirac $\delta$ 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. Comment: a serious flaw in the paper
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.01836 Zobrazit plný text záznamu View this record from Arxiv