2009 Fiscal Year Final Research Report
Study on the existence and stability of periodic solutions for delay dynamical systems
| Project/Area Number |
20740097
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Numazu College of Technology |
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Principal Investigator |
EGAMI Chikahiro Numazu College of Technology, 電子制御工学科, 助教 (90413781)
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| Project Period (FY) |
2008 – 2009
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| Keywords | 数理生物学 / Lotka-Volterra型方程式系 / HIV力学系 / Hopf分岐 / 写像度 |
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| Research Abstract |
This study examined the existence and stability of periodic solutions and also the effects of delays on the dynamics for systems of ordinary and delay differential equations which represent biological phenomena. The main results are classified into as follows : (i) For multi-species competitive systems with the nonlinearity called "Allee effect", incorporating various types of delays into models, the stability and permanence of system were analyzed. (ii) A new method for proving the existence of a Hopf bifurcation was established through the bifurcation analysis of a HIV model. This is particularly beneficial for models which consist of multiple valuables.
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