Project/Area Number  09640211 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Osaka Prefecture University 
Principal Investigator 
HARA Tadayuki Osaka Pref.Univ., Coll.of Eng., Professor, 工学部, 教授 (20029565)

CoInvestigator(Kenkyūbuntansha) 
MIYAZAKI Rinko Shizuoka Univ., Facul.of Eng., Associate Prof., 工学部, 助教授 (40244660)
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., 工学部, 助教授 (40175021)
MA Wanbiao Osaka Pref.Univ., Coll.of Eng., Assistant Prof., 工学部, 助手 (30305651)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Functional Differential Equation / Delay Differential Equation / Lotka Volterra Equation / PreyPredator Model / Global Asymptotic Stability / Permanence / Ivlev Type / Holling Type / 関数微分方程式 / 時間遅れを含む微分方程式 / ロトカ・ヴォルテラ方程式 / 被食者・捕食者モデル / 大域的漸近安定 / パーマネンス / イブレフ型 / ホリング型 / ルンゲ・クッタ法 / 微分差分方程式 / 指数漸近安定 
Research Abstract 
Main results of our research are as follows : 1. We have improved computer softwares DDEIRK and DDE2RK which were developed in our group several years ago for computer simulation of one and two dimensional differential equations with several delays. Now we obtained new computer softwares FDEIRK and FDE2RK which are applicable to delay differential equations with integral terms. We also developed computer softwares FDE4RKP and FDE4RKT for computer simulation of soluions of higher order dimensional delay differential equations with integral terms. 2. Using these softwares FDE4RKP and FDE4RKT, 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) A neccesary and sufficient condition for the exponential asymptotic stability of the zero solution of ndimenssional linear functional differential equations
… More
with variable coefficients. (2) A best possible sufficient condition for the asymptotic stability of the zero solution of one dimen sional nonlinear functional differential equations with variable coefficient. (3) Neccesary and sufficient conditions for the global asymptotic stability and the permanence of a LotkaVolterra type delay differential equations (4) Sufficient conditions for the asymptotic stability of a preypredator differential equation with delays expressed in integral terms. (5) Neccesary and sufficient conditions for the asymptotic stability and the asymptotic constant problem of a linear functional differential equation with delays expressed in Stieltjes integral. 3. We found neccesary and sufficient conditions for the existence of a limit cycle of preypredator differential equations without delay of Ivlev type and Holling type in mathematical ecology and succeeded to give mathematical proofs to these theorems. 3. 時間遅れのない生態系微分方程式系のうち、イブレフ型、ホリング型応答関数をもつ被食者・捕食者モデルが極限閉軌道をもつための必要十分条件の発見およびその証明の完成。 Less
