2013 Fiscal Year Final Research Report
Construction of the instability theory of two-dimensional nonautonomous systems and its application
| Project/Area Number |
23740115
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Okayama University of Science (2012-2013)
Miyakonojo National College of Technology (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 関数方程式 / 非自励系 / 不安定性 / 安定性 / リヤプノフの直接法 / 相平面解析 |
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| Research Abstract |
The known mathematical models are described by differential equations with periodic or constant coefficients in many cases. In this study, we targeted differential systems with time-varying coefficients (we call non-autonomous differential systems), which may correspond to other cases. In particular, I gave some sufficient conditions of uniform asymptotic stability and its instability for the linear systems and half-linear systems including a damped oscillator. The obtained results for uniform asymptotic stability can be expected strongly to be applied to giving a Lyapunov function with good properties. Therefore, the present study can contribute significantly to the perturbation problem and the robust stability problem.
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