| Project/Area Number |
11640210
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
HARA Tadayuki Osaka Pref.Univ., Coll.of Eng., Professor, 大学院・工学研究科, 教授 (20029565)
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| Co-Investigator(Kenkyū-buntansha) |
SAKATA Sadahisa Osaka Elec-Comm Univ.Coll.of Eng., Associate Prof., 工学部, 助教授 (60175362)
SUGIE Jitsuro Shimane Univ., Facul.of Sci.& Eng., Professor, 総合理工学部, 教授 (40196720)
YONEYAMA Toshiaki Osaka Pref.Univ., Coll.of Eng., Associate Prof., 大学院・工学研究科, 助教授 (40175021)
MA Wanbiao Shizuoka Univ., Facul.of Eng., Associate Prof., 工学部, 助教授 (30305651)
MIYAZAKI Rinko Shizuoka Univ., Facul.of Eng., Associate Prof., 工学部, 助教授 (40244660)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | Functional Differential Equation / Delay Differential Equation / Lotka-Volterra Equation / Prey-Predator Model / Global Asymptotic Stability / Permanence / Holling Type / Difference Equation / 時間遅れを含む微分方程式 / 大域的漸近安定 |
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| Research Abstract |
Main results of our research are as follows :
(I) We have improved computer software FDE2RK which was developed in our group two years ago for computer simulation of two dimensional differential equations with integral terms. In case the kernel of the integral does not depend on time variable, we improved our software and we can compute our differential
(II) Using the software FDE2RK, we studied the behavior of solutions of delay differential equations in mathematical ecology and found some interesting properties of solutions. We succeeded to give mathematical proofs to these properties. The typical results are as follows :
(1) Neccesary and sufficient conditions for the global asymptotic stability and the permanence of a Lotka-Volterra type differential equations with two delays
(2) Siability analysis of SIR epidemic models with distributed delays
(3) Stability analysis of two-dimensional neural net work with delays
(III)We found neccesary and sufficient conditions for the existence of a limit cycle and the global asymptotic stability of prey-predator differential equations without delay of Holling type in mathematical ecology and succeeded to give mathematical proofs to these theorems.
(VI) Oscillation theorems of the Riemann-Weber version of Euler differential equations with delay
(V) Using the software DDE2E, we studied the behavior of solutions of delay differential equations with piecewise constant arguments and difference equations with delays and found some interesting properties of solutions. We succeeded to give mathematical proofs to these properties. The typical results are as follows :
(1) Neccesary and sufficient conditions for the global asymptotic stability of a linear defference equation of higher order
(2) Neccesary and sufficient condition for the permanence of difference equations of Lotka-Volterra type
(3) Classification of the dynamics of 2-dimensional linear differential Equations with piecewise constant arguments
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