arXiv subjects

Tetsuya Ishiwata

Publications and source records attributed to Tetsuya Ishiwata.

2 recordsLinked to original sources

arXiv2021

Delay-induced blow-up in a planar oscillation model

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 a blow-up solution, 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.

math.DS↗

arXiv2019

Numerical analysis comparing ODE approach and level set method for evolving spirals by crystalline eikonal-curvature flow

In this paper, the evolution of a polygonal spiral curve by the crystalline curvature flow with a pinned center is considered with two view points, discrete model consist of an ODE system of facet lengths and a level set method. We investigate the difference of these models numerically by calculating the area of the region enclosed by these spiral curves. The area difference is calculated by the normalized L1 norm of the difference of step-like functions which are branches of arg(x) whose discontinuities are only on the spirals. We find the differences of the numerical results considered in this paper are very small even though the evolution laws of these models around the center and the farthest facet are slightly different.

math.NA↗