| Project/Area Number |
08640310
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | KYOTO SANGYO UNIVERSITY |
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Principal Investigator |
HOSONO Yuzo KYOTO SANGYO UNIVERSITY,DEPARTMENT OF INFORMATION AND COMMUNICATION SCIENCES,PROFESSOR, 工学部, 教授 (50008877)
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| Co-Investigator(Kenkyū-buntansha) |
TSUJII Yoshiki KYOTO SANGYO UNIVERSITY,DEPARTMENT OF COMPUTER SCIENCES,PROFESSOR, 理学部, 教授 (90065871)
石田 久 京都産業大学, 理学部, 教授 (10103714)
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| Project Period (FY) |
1996 – 1997
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| Project Status |
Completed (Fiscal Year 1997)
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| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1997: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1996: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | REACTION-DIFFUSION SYSTEM / TRAVELLING WAVE / KERMACK-MCKENDRIC MODEL / SINGULAR PERTURBATION / DHAR SAND PILE MODEL / PATTERN FORMATION / LOTKA-VOLTERRA COMPETITION MODEL / HETEROCLINIC ORBIT / ヘテロクリニック軌道 / 最小速度 / 時間空間パターン / ロトカーボルテラ2種競争系 / ケルマック-マッケンドリック伝染病モデル |
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| Research Abstract |
We are concened with the minimal speed of traveling wave fronts for a two species diffusion-competition model of Lotka-Volterra type. The 1989 paper by A.Okubo et al.employed this model to discuss the speed of invasion of gray squirrel by estimating the model parameters from field data, and predicted its speed by the use of a heuristic analytical argument. We investigate the conditions which assure the validity of their argument by singular perturbations and a geometric method and show numerically the existence of the realistic values of parameters for which their heuristic argument does not hold.
We also investigate the existence of traveling wave solutions for the infective-susceptible two component epidemic model. The model system is described by reaction-diffusion equations with the nonlinear reaction term of the classical Kermack-McKendric type. The diffusion coefficients of infectives and susceptibles are assumed to be nonnegative constants and d_1 d_2 respectively. By the shooting argument with the aid of the invariant manifold theory, we prove that there exists a positive constant c^<**> such that traveling wave solutions exist for any c<greater than or equal>c^<**>. The minimal wave speed c^<**> is shown to be independent of d_2 and to have the same value as for the case d_2=0.
Using the above method, we study the pattern formation model of bacteria colony proposed by M.Mimura et al.which has the same kind of nonlinearity as the Kermack-McKendric type. We have analyzed the local properties of the traveling wave equations and obtained numerically the properties of the 4-dimensional heteroclinic orbits for traveling waves. These analysis give the foundation of further research of pattern formation of bacteria colony.
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