2013 Fiscal Year Final Research Report
Consideration on a kind of difference equations and differential equations with time delay
| Project/Area Number |
23540163
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Tokyo University of Science |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
FUKUDA Akiko 東京理科大学, 理学部, 助教 (70609297)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | 差分方程式 / 離散可積分系 / 数理生物モデル / 遅延微分方程式 / 数値計算 |
|---|
| Research Abstract |
We obtained a new eigenvalue algorithm based on the discrete hungry Lotka-Volterra (dhLV) system of multiplicative type and discussed its convergence with the help of the center manifold theory. Another idea to derive the conserved quantities of the dhLV system was found only using the properties of the characteristic polynomial of the corresponding matrix. Moreover, we are concerned with the discrete epidemic models with and without time delay. Applying a proper discretization, the positivity of the solution for the discrete model can be kept, and then the ultra-discretized epidemic models can be easily derived. We investigated the global properties of the solution for such ultra-discretized epidemic models.
|
