Accuracy and stability for delayed integral and differential equations and their discrete equations

• Project/Area Number: 19540229
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Waseda University
• Principal Investigator: MUROYA Yoshiaki Waseda University, 理工学術院, 教授 (90063718)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 関数方程式の大域理論 / 数理生態学 / 数理モデル / 力学系

Research Abstract

遅れを持つ微分方程式やその離散化方程式系の大域漸近安定性の研究、特に、2種の非自励、遅れを持つ共生Lotka-Volterra方程式系の、遅れに関係しないpermanence 条件の導出、2種類のcontractivity条件、semi-contractive関数の導入とそのClarkモデルへの応用、Gopalsamy and Liuのconjectureの肯定的解決とその拡張、infection項を持つ離散人口モデルの基本再生産数、Volterra差分方程式の大域漸近安定性などの研究成果を得た。

Research Products

• [Journal Article] Permanence for two species nonautonomous Lotka-Volterra cooperative systems with delays (2009)
  • Author(s): Y. Nakata and Y. Muroya
  • Journal Title: Nonlinear Analyis RWA (2009)
  • Peer Reviewed
• [Journal Article] Contractivity for nonautonomous logistic equation with piecewise constant delays, CP1124, Mathematical Models in Engineering, Biology, and Medicine, Proceedings of the International Conference on Boundary Value Problem, (2009)
  • Author(s): Y. Nakata, M. Kuroda and Y. Muroya
  • Journal Title: edited by A. Cabada, E. Liz, and J.J. Nieto Pages: 254-263
  • Peer Reviewed
• [Journal Article] Global stability for a class of difference equations (2009)
  • Author(s): Y. Muroya and E. Ishiwata
  • Journal Title: J. Compu.Appl.Math 228 Pages: 561-570
• [Journal Article] New global stability conditions for a classes of difference equations (2009)
  • Author(s): Y. Muroya, E. Ishiwata and N. Guglielmi
  • Journal Title: Frontiers of Mathematics in China 4 Pages: 131-154
  • Peer Reviewed
• [Journal Article] On collocation methods for delay differential and Volterra integral equations with proportional delay (2009)
  • Author(s): E. Ishiwata and Y. Muroya
  • Journal Title: Fontiers of Mathematics in China 4 Pages: 89-111
  • Peer Reviewed
• [Journal Article] sufficient condition for the global asymptotic stability of a class of logistic equations with piecewise constant delay (2009)
  • Author(s): H. Li, Y. Muroya and R. Yuan, A
  • Journal Title: Nonlinear Analysis RWA 10 Pages: 244-253
  • Peer Reviewed
• [Journal Article] A general discrete time model of population dynamics in the presence of an infection (2009)
  • Author(s): G. Izzo, Y. Muroya, A. Veoohio
  • Journal Title: Discrete Dynamics in Nature and Society (accepted)
  • Peer Reviewed
• [Journal Article] Contractivity for nonautonomous logistic equation with piecewise constant delays (2009)
  • Author(s): Y. Nakata, M. Kuroda, Y. Muroya
  • Journal Title: Proceedings of BVP (accepted)
  • Peer Reviewed
• [Journal Article] Permanence for two species nonautonomous Lotka-Volterra cooperative systems with delays (2009)
  • Author(s): Y. Nakata, Y. Muroya
  • Journal Title: Nonlinear Analysis RWA
  • Peer Reviewed
• [Journal Article] Global stability for a class of difference equations (2009)
  • Author(s): Y. Muroya, E. Ishiwata
  • Journal Title: J. Comput. Appl. Math.
  • Peer Reviewed
• [Journal Article] New global stability conditions for a classes of difference equations (2009)
  • Author(s): Y. Muroya, E. Ishiwata, N. Guglielmi
  • Journal Title: Frontiers of Mathematics in China 4 Pages: 131-154
  • Peer Reviewed
• [Journal Article] On collooation methods for delay differential and Volterra integral equations with proportional delay, delay (2009)
  • Author(s): E. Ishiwata, Y. Muroya
  • Journal Title: Frontiers of Mathematics in China 4 Pages: 89-111
  • Peer Reviewed
• [Journal Article] A sufficient condition for the global asymptotic stability of a class of logistic equations with piecewise constant delay (2009)
  • Author(s): H. Li, Y. Muroya, R. Yuan
  • Journal Title: Nonlinear Analysis RWA 10 Pages: 244-253
  • Peer Reviewed
• [Journal Article] New contractivity condition in a population model with piecewise constant arguments (2008)
  • Author(s): Y. Muroya
  • Journal Title: J. Math. Anal. Appl 346 Pages: 65-81
  • Peer Reviewed
• [Journal Article] A super-attainable order in collocation methods for differential equations with proportional delay (2008)
  • Author(s): E. Ishiwata, Y. Muroya and H. Brunner
  • Journal Title: Appl. Math. Comput 198 Pages: 227-236
• [Journal Article] New contraotivity condition in a population model with piecewise constant arguments (2008)
  • Author(s): Y. Muroya
  • Journal Title: J. Math. Anal. Appl. 346 Pages: 65-81
  • Peer Reviewed
• [Journal Article] Asymptotic behavior of solutions for nonlinear Volterra discrete equations (2008)
  • Author(s): E. Messina, Y. Muroya, E. Russo, A. Vecchio
  • Journal Title: Discrete Dynamics in Nature and Society ID 867623
  • Peer Reviewed
• [Journal Article] A super-attainable order in collocation methods for differential equations with proportional delay (2008)
  • Author(s): E. Ishiwata, Y. Muroya, H. Brunner
  • Journal Title: Appl. Math. Comput. 198 Pages: 227-236
  • Peer Reviewed
• [Journal Article] A super-attainable order in collocation methods for differential equations with proportional delay (2008)
  • Author(s): E.Ishiwata, Y.Muroya and H.Brunner
  • Journal Title: Appl.Math.Comput 198 Pages: 227-236
  • Peer Reviewed
• [Journal Article] Global stability for nonlinear difference equations with variable coefficients (2007)
  • Author(s): Y. Muroya, E. Ishiwata and N. Guglielmi
  • Journal Title: J. Math. Anal. Appl 334 Pages: 232-247
  • Peer Reviewed
• [Journal Article] Global attractivity for discrete models of nonautonomous logistic equations (2007)
  • Author(s): Y. Muroya
  • Journal Title: Comput. Math. Appl 53 Pages: 1059-1073
  • Peer Reviewed
• [Journal Article] Rational approximation method for delay differential equations with proportional delay (2007)
  • Author(s): E. Ishiwata, Y. Muroya
  • Journal Title: Appl. Math. Comput 187 Pages: 741-747
  • Peer Reviewed
• [Journal Article] Persistence and global stability in discrete models of Lotka-Volterra type (2007)
  • Author(s): Y. Muroya
  • Journal Title: J. Math. Anal. Appl 330 Pages: 24-33
  • Peer Reviewed
• [Journal Article] Global attractivity for discrete Clark model $x_{n+1}=q x_n+(1-q)g(x_{n-k})$ (2007)
  • Author(s): Y. Muroya and E. Ishiwata
  • Journal Title: Proceedings of the Furth Internaional Conference on Nonlinear Analysis and Convex Analysis (2005 Okinawa) Pages: 387-398
  • Peer Reviewed
• [Journal Article] Global stability for separable nonlinear delay differential systems (2007)
  • Author(s): Y. Muroya
  • Journal Title: J. Math. Anal. Appl 236 Pages: 372-389
  • Peer Reviewed
• [Journal Article] A global stability criterion in scalar delay differential equations (2007)
  • Author(s): Y. Muroya
  • Journal Title: J. Math. Anal. Appl 236 Pages: 209-227
  • Peer Reviewed
• [Journal Article] Stability of Volterra difference equations (2007)
  • Author(s): Y. Muroya
  • Journal Title: 数理解析研究所講究録 1551 Pages: 105-110
  • Peer Reviewed
• [Journal Article] Global stability for nonlinear difference equations with variable coefficients (2007)
  • Author(s): Y.Muroya, E.Ishiwata and N.Guglielmi
  • Journal Title: J.Math.Anal.Appl. 334 Pages: 232-247
  • Peer Reviewed
• [Journal Article] Global attractivity for discrete models of nonautonomous logistic equations (2007)
  • Author(s): Y.Muroya
  • Journal Title: Comput.Math.Appl. 53 Pages: 1059-1073
  • Peer Reviewed
• [Journal Article] Rational approximation method for delay differential equations with proportional delay (2007)
  • Author(s): E.Isiwata, and Y.Muroya
  • Journal Title: Appl.Math.Comput. 187 Pages: 741-747
  • Peer Reviewed
• [Journal Article] Persistence and global stability discrete models of Lotka Volterra type (2007)
  • Author(s): Y.Muroya
  • Journal Title: J.Math.Anal.Appl. 330 Pages: 24-33
  • Peer Reviewed
• [Journal Article] Global attractivity for discrete Clark model x{n+1}=q x n+(1-q)g(x_{n-k}) (2007)
  • Author(s): Y.Muroya and E.Ishiwata
  • Journal Title: Proceedings of the Fourth International Conference on Nonlinear Analysis and Convex Analysis(2005Okinawa) Pages: 387-398
  • Peer Reviewed
• [Journal Article] Global stability for separable nonlinear delay differential equations (2007)
  • Author(s): Y.Muroya
  • Journal Title: J.Math.Anal.Appl. 236 Pages: 372-389
  • Peer Reviewed
• [Journal Article] A global stability criterion in scalar delay differential equations (2007)
  • Author(s): Y.Muroya
  • Journal Title: J.Math.Anal.Appl. 236 Pages: 209-227
  • Peer Reviewed
• [Journal Article] Stability of Volterra difference equations (2007)
  • Author(s): Y.Muroya and E.Ishiwata
  • Journal Title: 数理解析研究所講究録 1551 Pages: 105-110
• [Journal Article] general discrete time model of population dynamics in the presence of an infection
  • Author(s): G. Izzo, Y. Muroya and A. Vecchio, A
  • Journal Title: accepted in Discrete Dynamics in Nature and Society
  • Peer Reviewed
• [Journal Article] Asymptotic behavior of solutions for nonlinear Volterra discrete equations
  • Author(s): E. Messina, Y. Muroya, E. Russo and A. Vecchio
  • Journal Title: Discrete Dynamics in Nature and Society vol Article ID 867623
  • Peer Reviewed
• [Journal Article] Global stability for a class of difference equations
  • Author(s): Y.Muroya and E.Ishiwata
  • Journal Title: J.Comput.Appl.Math.
  • Peer Reviewed
• [Journal Article] A sufficient condition for the global asymptotic stability of a class of logistic equations with piecewise constant delay
  • Author(s): H.Li, Y.Muroya and R.Yuan
  • Journal Title: Nonlinear Analysis RWA
  • Peer Reviewed
• [Presentation] 区分的定数遅れを持つロジスティック方程式の大域漸近安定性 (2008)
  • Author(s): 室谷義昭
  • Organizer: 2008年度日本応用数理学会年会
  • Place of Presentation: 東大柏キャンパス
  • Year and Date: 2008-09-19
• [Presentation] On global stability in a PoPulation model with piecewise constant delays (2008)
  • Author(s): Y.Muroya
  • Organizer: Numerical group seminar at University of Naples
  • Place of Presentation: University of Naples
  • Year and Date: 2008-04-07
• [Presentation] Global stability for a class of discrete models (2007)
  • Author(s): Y.Muroya, joint work with E.Ishiwata and N.Guglielmi
  • Organizer: International Workshop on Numerical Analysis and Computational Equations, Functional Differential and Integral Equations
  • Place of Presentation: Hong Kong
  • Year and Date: 2007-12-06
• [Presentation] Global attractivity for nonlinear difference equations with variable coefficients (2007)
  • Author(s): Y.Muroya, joint work with E.Ishiwata
  • Organizer: 「生物数学の理論とその応用」研究集会
  • Place of Presentation: 京大数理解析研
  • Year and Date: 2007-08-31
• [Presentation] Uniform stability for a wide class of difference equations (2007)
  • Author(s): Y.Muroya, joint work with E.Ishiwata
  • Organizer: International Conference on Scientific Computation And Differential Equations
  • Place of Presentation: SainT-Malo,France
  • Year and Date: 2007-07-13
• [Remarks]
  • URL: https://www.wnp7.waseda.jp/Rdb/app/ip/ipi0201.html