Open AccessOptimal linear stability condition for scalar differential equations with distributed delay
Author(s) -
Samuel Bernard,
Fabien Crauste
Publication year - 2015
Publication title -
discrete and continuous dynamical systems - b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2015.20.1855
Subject(s) - delay differential equation , stability theory , nonlinear system , mathematics , scalar (mathematics) , stability (learning theory) , differential equation , control theory (sociology) , distributed parameter system , linear stability , mathematical analysis , exponential stability , computer science , physics , geometry , control (management) , quantum mechanics , machine learning , artificial intelligence
International audienceLinear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote oscillations around steady states, and their stability depends on the particular shape of the delay distribution. Since in applications the mean delay is often the only reliable information available about the distribution, it is desirable to find conditions for stability that are independent from the shape of the distribution. We show here that for a given mean delay, the linear equation with distributed delay is asymptotically stable if the associated differential equation with a discrete delay is asymptotically stable. We illustrate this criterion on a compartment model of hematopoietic cell dynamics to obtain sufficient conditions for stability
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