Bifurcation-based stability analysis of hybrid dynamical systems with smooth approximating mode switching functions
| Project/Area Number |
18K11460
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 61040:Soft computing-related
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| Research Institution | Utsunomiya University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | カオス |
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| Outline of Final Research Achievements |
The author analyzed bifurcation of periodic motion when we approximate the dry friction of the mechanical model to generate a stick-slip motion in the smooth function as an example of hybrid dynamical systems. The author applied periodic perturbation to the belt speed, tracked the cycle point, and created a 2-parameter bifurcation diagram of 1/1, 2/1, and, 3/1 entrainment region. As a result, it was found that stable periodic point, saddle, and, unstable periodic points coexist in entrainment region, and a nonlinear phenomena such as period-doubling bifurcations, chaos, and so on are observed at stable periodic point. In addition, it was found that adjacent n/1 entrainment regions were connected through two Neimark-Sacker bifurcation curves and the period-doubling bifurcation curve of saddle.
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| Academic Significance and Societal Importance of the Research Achievements |
機械工学、非線形動力学、分岐理論の３分野の知識を導入して、機械工学系の安定性解析を行った。非線形動力学分野でしばしば用いられる、分岐理論に基づく安定性解析法を応用して得られた研究成果は十分に学術的意義がある。
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Report
(4 results)
Research Products
(4 results)
