2000 Fiscal Year Annual Research Report

コンピューターシミュレーションを併用した関数微分方程式の定性的研究

Research Project

Project/Area Number	11640210
Research Institution	Osaka Prefecture University
Principal Investigator	原惟行大阪府立大学, 工学研究科, 教授 (20029565)
Co-Investigator(Kenkyū-buntansha)	坂田定久大阪電気通信大学, 工学部, 助教授 (60175362) 杉江実郎島根大学, 総合理工学部, 教授 (40196720) 米山俊昭大阪府立大学, 工学研究科, 助教授 (40175021) 馬万彪静岡大学, 工学部, 助教授 (30305651) 宮崎倫子静岡大学, 工学部, 助教授 (40244660)
Keywords	関数微分方程式 / 時間遅れをもつ微分方程式 / ロトカ・ヴォルテラ方程式 / 被食者・捕食者モデル / 大域的漸近安定性 / パーマネンス / ホリング型 / 差分方程式
Research Abstract	(I)積分項を含んだ関数微分方程式系の解のグラフィックソフトFDE2RKにおいて積分項の核が時間に依存しない場合のプログラムを大幅に改良した。これにより積分項を含む場合の計算速度を飛躍的にスピードアップできた。 (II)上記のグラフィックソフトFDE2RKを用いて時間遅れをもつ生態系微分方程式の解軌道をグラフィック化し解の特性を調べ、抽出したいくつかの解の性質に数学的証明を与えることに成功した。それらのうち代表的なものは以下の通りである: (1)2個の時間遅れをもつロトカ・ヴォルテラ微分方程式の大域的漸近安定性とパーマネンスの必要十分条件 (2)積分項で表される時間遅れをもつSIR伝染病モデルの安定解析 (3)時間遅れをもつ2次元ニューラルネットワークの安定解析 (III)時間遅れのない生態系微分方程式系のうち、ホリング型応答関数をもつ被食者・捕食者モデルにおけるリミットサイクルの一意性の証明。 (IV)オイラー型微分方程式に対するリーマン・ウェーバー型振動定理の証明および2階非線形微分方程式の解の非振動定理の証明。 (V)区分的に一定な時間遅れをもつ微分方程式および遅れをもつ差分方程式のコンピューターシミュレーションソフトDDE2Eを用い解軌道をグラフィック化し、解の特性を調べ、抽出したいくつかの解の性質に数学的証明を与えることに成功した。それらのうち代表的なものは以下の通りである: (1)高階1次元線形差分方程式の零解の漸近安定性に関する必要十分条件 (2)ロトカ・ヴォルテラ差分方程式系のパーマネンスに関する必要十分条件 (3)区分的に一定な時間遅れをもつ2次元線形微分方程式の解のダイナミックスの分類

Research Products
(27 results)

All Other

All Publications (27 results)

[Publications] H.Matsunaga,R.Miyazaki and T.Hara: "Global attractivity results for nonlinear delay differential equations"Journal of Mathematical Analysis and Applications. 234. 77-90 (1999)
[Publications] Y.Saito,T.Hara and W.Ma: "Necessary and sufficient conditions for permanence and global stability of a Lotka-Volterra system with two delays"Journal of Mathematical Analysis and Applications. 236. 534-556 (1999)
[Publications] Y.Takeuchi and W.Ma: "Stability analysis on a delayed SIR epidemic model with density dependent birth process"Dynamics of Continuous, Discrete and Impulsive Systems. 5. 171-184 (1999)
[Publications] J.Sugie and M.Katayama: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Analysis. 38. 105-121 (1999)
[Publications] R.Miyazaki: "Analysis of characteristic roots of delay-differential systems"Dynamics of Continuous, Discrete and Impulsive Systems. 5. 195-207 (1999)
[Publications] H.Matsunaga and T.Hara: "The asymptotic stability of a two-dimensional linear delay difference equation"Dynamics of Continuous, Discrete and Impulsive Systems. 6. 465-473 (1999)
[Publications] T.Hara,R.Miyazaki and T.Morii: "Asymptotic periodic solutions for linear differential-difference equations with N delays and Hopf bifurcations"Funkcialaj Ekvacioj. 43. 193-212 (2000)
[Publications] S.Sakata and T.Hara: "Dynamics of a linear differential system with piecewise constant argument"Dynamics of Continuous, Discrete and Impulsive Systems. 7. 585-594 (2000)
[Publications] R.Ogita,H.Matsunaga and T.Hara: "Asymptotic stability condition for a class of linear delay difference equations of higher order"Journal of Mathematical Analysis and Applications. 248. 83-96 (2000)
[Publications] W.Ma,T.Hara and Y.Takeuchi: "Stability of a 2-dimensional neural network with time delays"Journal of Biological Systems. 8. 177-193 (2000)
[Publications] S.Sakata: "Stability sets for linear differential difference equations with two delays"Dynamic Systems and Applications. 9. 569-594 (2000)
[Publications] Y.Takeuchi,W.Ma and E.Beretta: "Global asymptotic properties of a delay SIR epidemic model with varying population size and finite incubation times"Nonlinear Analysis. 42. 931-947 (2000)
[Publications] J.Sugie: "Uniqueness of limit cycles in a predator-prey system of Holling-type functional response"Quarterly of Applied Mathematics. 58. 577-590 (2000)
[Publications] J.Sugie and M.Iwasaki: "Oscillation of the Riemann-Weber version of Euler differential equations with delay"Georgian Mathematical Journal. 7. 577-584 (2000)
[Publications] T.Naito,N.V.Minh,R.Miyazaki and J.Shin: "A decomposition theorem for bounded solutions and the existence of periodic solutions of periodic differential equations"Journal of Differential Equations. 160. 260-282 (2000)
[Publications] J.Sugie and K.Kita: "Oscillation criteria for second order nonlinear differential equations of Euler type"Journal of Mathematical Analysis and Applications. 253. 414-439 (2001)
[Publications] H.Matsunaga,T.Hara and S.Sakata: "Global attractivity for a logistic equation with piecewise constant argument"Nonlinear Differential Equations and Applications. (in press).
[Publications] Y.Saito,W.Ma and T.Hara: "A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays"Journal of Mathematical Analysis and Applications. (in press).
[Publications] H.Matsunaga,T.Hara and S.Sakata: "Global attractivity for a nonlinear difference equation with variable delay"Computers & Mathematics with Applications. (accepted).
[Publications] T.Hara and S.Sakata: "Star-shaped periodic solutions for x'(t)=-a{1-|x(t)|^‥2}R(θ)x([t])"Nonlinear Analysis. (accepted).
[Publications] J.Sugie: "Lienard dynamics with an open limit orbit"Nonlinear Differential Equations and Applications. (accepted).
[Publications] J.Sugie: "A nonoscillation theorem for second-order nonlinear differential equations with decaying coefficients"The Bulletin of the London Mathematical Society. (accepted).
[Publications] T.Naito,N.V.Minh,R.Miyazaki and Y.Hamaya: "Boundedness and almost periodicity in dynamical systems"Journal of Difference Equations and Applications. (accepted).
[Publications] E.Beretta,T.Hara,W.Ma and Y.Takeuchi: "Global asymptotic stability of an SIR epidemic model with distributed time delay"Nonlinear Analysis. (accepted).
[Publications] T.Hara and S.Sakata: "Dynamics of a delay differential system with periodically oscillatory coefficients"Nonlinear Analysis. (accepted).
[Publications] J.Sugie,N.Yamaoka and Y.Obata: "Nonoscillation theorems for a nonlinear self-adjoint differential equation"Nonlinear Analysis. (accepted).
[Publications] Y.Saito,T.Hara and W.Ma: "Harmless delays for permanence and impersistence of Lotka-Volterra discrete predator-prey system"Nonlinear Analysis. (accepted).

2000 Fiscal Year Annual Research Report

コンピューターシミュレーションを併用した関数微分方程式の定性的研究

Principal Investigator

原 惟行 大阪府立大学, 工学研究科, 教授 (20029565)

Research Products

[Publications] H.Matsunaga,R.Miyazaki and T.Hara: "Global attractivity results for nonlinear delay differential equations"Journal of Mathematical Analysis and Applications. 234. 77-90 (1999)

[Publications] Y.Saito,T.Hara and W.Ma: "Necessary and sufficient conditions for permanence and global stability of a Lotka-Volterra system with two delays"Journal of Mathematical Analysis and Applications. 236. 534-556 (1999)

[Publications] Y.Takeuchi and W.Ma: "Stability analysis on a delayed SIR epidemic model with density dependent birth process"Dynamics of Continuous, Discrete and Impulsive Systems. 5. 171-184 (1999)

[Publications] J.Sugie and M.Katayama: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Analysis. 38. 105-121 (1999)

[Publications] R.Miyazaki: "Analysis of characteristic roots of delay-differential systems"Dynamics of Continuous, Discrete and Impulsive Systems. 5. 195-207 (1999)

[Publications] H.Matsunaga and T.Hara: "The asymptotic stability of a two-dimensional linear delay difference equation"Dynamics of Continuous, Discrete and Impulsive Systems. 6. 465-473 (1999)

[Publications] T.Hara,R.Miyazaki and T.Morii: "Asymptotic periodic solutions for linear differential-difference equations with N delays and Hopf bifurcations"Funkcialaj Ekvacioj. 43. 193-212 (2000)

[Publications] S.Sakata and T.Hara: "Dynamics of a linear differential system with piecewise constant argument"Dynamics of Continuous, Discrete and Impulsive Systems. 7. 585-594 (2000)

[Publications] R.Ogita,H.Matsunaga and T.Hara: "Asymptotic stability condition for a class of linear delay difference equations of higher order"Journal of Mathematical Analysis and Applications. 248. 83-96 (2000)

[Publications] W.Ma,T.Hara and Y.Takeuchi: "Stability of a 2-dimensional neural network with time delays"Journal of Biological Systems. 8. 177-193 (2000)

[Publications] S.Sakata: "Stability sets for linear differential difference equations with two delays"Dynamic Systems and Applications. 9. 569-594 (2000)

[Publications] Y.Takeuchi,W.Ma and E.Beretta: "Global asymptotic properties of a delay SIR epidemic model with varying population size and finite incubation times"Nonlinear Analysis. 42. 931-947 (2000)

[Publications] J.Sugie: "Uniqueness of limit cycles in a predator-prey system of Holling-type functional response"Quarterly of Applied Mathematics. 58. 577-590 (2000)

[Publications] J.Sugie and M.Iwasaki: "Oscillation of the Riemann-Weber version of Euler differential equations with delay"Georgian Mathematical Journal. 7. 577-584 (2000)

[Publications] T.Naito,N.V.Minh,R.Miyazaki and J.Shin: "A decomposition theorem for bounded solutions and the existence of periodic solutions of periodic differential equations"Journal of Differential Equations. 160. 260-282 (2000)

[Publications] J.Sugie and K.Kita: "Oscillation criteria for second order nonlinear differential equations of Euler type"Journal of Mathematical Analysis and Applications. 253. 414-439 (2001)

[Publications] H.Matsunaga,T.Hara and S.Sakata: "Global attractivity for a logistic equation with piecewise constant argument"Nonlinear Differential Equations and Applications. (in press).

[Publications] Y.Saito,W.Ma and T.Hara: "A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays"Journal of Mathematical Analysis and Applications. (in press).

[Publications] H.Matsunaga,T.Hara and S.Sakata: "Global attractivity for a nonlinear difference equation with variable delay"Computers & Mathematics with Applications. (accepted).

[Publications] T.Hara and S.Sakata: "Star-shaped periodic solutions for x'(t)=-a{1-|x(t)|^‥2}R(θ)x([t])"Nonlinear Analysis. (accepted).

[Publications] J.Sugie: "Lienard dynamics with an open limit orbit"Nonlinear Differential Equations and Applications. (accepted).

[Publications] J.Sugie: "A nonoscillation theorem for second-order nonlinear differential equations with decaying coefficients"The Bulletin of the London Mathematical Society. (accepted).

[Publications] T.Naito,N.V.Minh,R.Miyazaki and Y.Hamaya: "Boundedness and almost periodicity in dynamical systems"Journal of Difference Equations and Applications. (accepted).

[Publications] E.Beretta,T.Hara,W.Ma and Y.Takeuchi: "Global asymptotic stability of an SIR epidemic model with distributed time delay"Nonlinear Analysis. (accepted).

[Publications] T.Hara and S.Sakata: "Dynamics of a delay differential system with periodically oscillatory coefficients"Nonlinear Analysis. (accepted).

[Publications] J.Sugie,N.Yamaoka and Y.Obata: "Nonoscillation theorems for a nonlinear self-adjoint differential equation"Nonlinear Analysis. (accepted).

[Publications] Y.Saito,T.Hara and W.Ma: "Harmless delays for permanence and impersistence of Lotka-Volterra discrete predator-prey system"Nonlinear Analysis. (accepted).

原惟行大阪府立大学, 工学研究科, 教授 (20029565)