Elucidation of global dynamics for damped oscillators and dissipative wave equations and its application to biology

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400165
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Shimane University
• Principal Investigator: Sugie Jitsuro 島根大学, 総合理工学研究科, 教授 (40196720)
• Co-Investigator(Renkei-kenkyūsha): MATSUNAGA HIDEAKI 大阪府立大学, 工学研究科, 准教授 (40332960) ; SAITO YASUHISA 島根大学, 総合理工学研究科, 准教授 (30402241) ; ONITSUKA MASAKAZU 岡山理科大学, 理学部, 講師 (20548367)
• Research Collaborator: Fan Meng 東北師範大学, 数学与統計学院, 教授 ; Wu Fentao 東北師範大学, 数学与統計学院, 教授
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 減衰振動子 / 一様漸近安定性 / 大域的漸近安定性 / 振動性 / 差分方程式 / 半分線形微分方程式 / 生態系モデル / 相平面解析

Outline of Final Research Achievements

The global dynamics of various damped oscillators and difference equations were clarified from the viewpoint of stability and oscillation of the equilibrium point. Among the obtained research results, that related to the global asymptotic stability of the damped linear oscillator was applied to a time-varying Lotka-Volterra predator-prey model. The global asymptotic stability of the damped super-linear oscillator which was the equation of motion of the object in underwater was also discussed. Furthermore, the global asymptotic stability of the coupled oscillator whose coefficient varies with time and the convergence of radially symmetric solutions of quasi-linear elliptic equations were studied.

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