TY - JOUR

T1 - Delay-induced blow-up in a planar oscillation model

AU - Eremin, Alexey

AU - Ishiwata, Emiko

AU - Ishiwata, Tetsuya

AU - Nakata, Yukihiko

N1 - Eremin, A., Ishiwata, E., Ishiwata, T. et al. Delay-induced blow-up in a planar oscillation model. Japan J. Indust. Appl. Math. 38, 1037–1061 (2021). https://doi.org/10.1007/s13160-021-00475-x

PY - 2021/9

Y1 - 2021/9

N2 - 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.

AB - 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.

KW - Blow-up of solutions

KW - Delay differential equations

KW - Periodic solutions

KW - DIFFERENTIAL-EQUATIONS

KW - INTEGRODIFFERENTIAL EQUATIONS

KW - TIME

UR - http://www.scopus.com/inward/record.url?scp=85111169245&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0919515a-a1de-3414-8a2d-71c2b9f08965/

U2 - 10.1007/s13160-021-00475-x

DO - 10.1007/s13160-021-00475-x

M3 - Article

AN - SCOPUS:85111169245

VL - 38

SP - 1037

EP - 1061

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 3

ER -