Delay-induced blow-up in a planar oscillation model View Full Text


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Article Info

DATE

2021-07-22

AUTHORS

Alexey Eremin, Emiko Ishiwata, Tetsuya Ishiwata, Yukihiko Nakata

ABSTRACT

In this paper we study a system of delay differential equations from the viewpoint of a finite time blow-up of the solution. We prove that the system admits blow-up solutions, no matter how small the length of the delay is. In the non-delay system every solution approaches to a stable unit circle in the plane, thus time delay induces blow-up of solutions, which we call “delay-induced blow-up” phenomenon. Furthermore, it is shown that the system has a family of infinitely many periodic solutions, while the non-delay system has only one stable limit cycle. The system studied in this paper is an example that arbitrary small delay can be responsible for a drastic change of the dynamics. We show numerical examples to illustrate our theoretical results. More... »

PAGES

1037-1061

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s13160-021-00475-x

DOI

http://dx.doi.org/10.1007/s13160-021-00475-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1139870884


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