컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0539 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Ordinary Differential Equations / Dynamical Systems (SS-10) |
| 영문제목 (Title(Eng.)) |
Asymptotic constancy and convergent speeds of a delay differential system |
| 저자(Author(s)) |
Rinko Miyazaki1, Keita Ashizawa2 Shizuoka University1, Maizuru National College of Technology2 |
| 초록본문(Abstract) | The aim of this work is to expose some mathematical properties in complex networks. In particular, we focus on transmission delays and network topologies. In [1], we proved asymptotic constancy of the following a simple delay differential system $$ x'_i(t)=\alpha_i\{-x_i(t)+\frac{\sum_{j=1}^n b_{ij}x_j(t-\tau_j)}{\sum_{j=1}^n b_{ij}}\},\qquad(i=1,2,\ldots,n) $$ where $\alpha_i>0$ and $\tau_i\ge0$ are constants and $B:=(b_{ij})$ is an $n\times n$ binary matrix. In the system, we can interpret the matrix $B$ as a network topology and $\tau_i$ ($i=1,2,\ldots, n$) as transmission delays. In this talk, we give a new classification of the network topologies and a result on influences of the transmission delays and the network topologies on the asymptotic behavior of the solutions. Reference [1] K . Ashizawa and R. Miyazaki, Asymptotic constancy for a linear differential system with multiple delays, \textit{Applied Math. Lett.}, 19, (2006), 1390--1394. |
| 분류기호 (MSC number(s)) |
34D05, 34K06 |
| 키워드(Keyword(s)) | delay differential equations, asymptotic constancy |
| 강연 형태 (Language of Session (Talk)) |
English |