Density Evolution Under Delayed Dynamics

Losson, Jérôme; Mackey, Michael C.; Taylor, Richard J. K.; Tyran‐Kamińska, Marta

doi:10.1007/978-1-0716-1072-5

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2024

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Cited by 2 publications

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“…Rather it is of prime scientific interest because of the increasing prevalence of studies of systems whose dynamics contain significant time delays, and the fact that we have no way of theoretically treating these systems. Various approximations are available, and we have briefly discussed some of these while mentioning that there is a much more extensive consideration of these 21 . We have also presented a tentative new approach to the problem in Section VI.…”

Section: Discussionmentioning

confidence: 99%

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How can we describe density evolution under delayed dynamics?

Mackey

Tyran‐Kamińska

2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done numerically and the interesting dynamics that have emerged, and the largely unsuccessful attempts that have been made to analytically treat the evolution of densities in differential delay equations. We also present a new approach to the problem and illustrate it with a simple example.

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Section: Discussionmentioning

confidence: 99%

“…(30) Equations ( 29)- (30) apparently answer the question posed above about the evolution of probability measures for delay differential equations. However, this is illusory 21 since they provide only a symbolic restatement of the problem. Everything that is specific to a given differential delay equation is contained in S −1 t .…”

Section: How To Formulate?mentioning

confidence: 99%