Delay-induced blow-up in a planar oscillation model

Alexey Eremin, Emiko Ishiwata, Tetsuya Ishiwata, Yukihiko Nakata

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1037-1061
Number of pages25
JournalJapan Journal of Industrial and Applied Mathematics
Volume38
Issue number3
DOIs
Publication statusPublished - 2021 Sep

Keywords

  • Blow-up of solutions
  • Delay differential equations
  • Periodic solutions

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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