Delay-induced blow-up in a planar oscillation model
Delay-induced blow-up in a planar oscillation model
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DOI：
10.1007/s13160-021-00475-x
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发表时间：
2018-03
影响因子：
0.9
通讯作者：
A. Eremin;E. Ishiwata;T. Ishiwata;Y. Nakata
中科院分区：
文献类型：
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作者：
A. Eremin;E. Ishiwata;T. Ishiwata;Y. Nakata
本文从解的有限时间爆破的观点研究一类时滞微分方程组。我们证明了系统允许爆破的解决方案，无论多么小的延迟的长度。在非时滞系统中，每个解都趋近于平面上的一个稳定单位圆，时滞导致解的爆破，我们称之为时滞诱导爆破现象。进一步证明了该系统存在一族无穷多个周期解，而非时滞系统只有一个稳定的极限环。本文所研究的系统是一个例子，任意小的延迟可以负责一个剧烈的变化的动态。我们用数值例子来说明我们的理论结果。
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.