2001 Fiscal Year Final Research Report Summary
Studies on the stability of a Leontief dynamic model with delays
| Project/Area Number |
12630011
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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 |
経済理論
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| Research Institution | The University of Tokushima |
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Principal Investigator |
MAYUMI Kozo Fac. of IAS, The University of Tokushima, Professor, 総合科学部, 教授 (40253182)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Leontief model / Delay model / Stability / Dynamic model / Transcendental equation / Laplace transform |
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| Research Abstract |
First, we investigatd the following model
a_<11>x_1(t) - a_<12>x_2(t) - B_<11>(dx_1(t-γ_1)) / (dt) - B_<12> (dx_2(t-γ_2)) / (dt) = z_1(t), (1)
-a_<12>x_1(t) + a_<22>x_2(t) - B_<21>(dx_1(t - γ_1)) / (dt) - B_<22>(dx_2(t - γ_2)) / (dt) = z_2(t), (2)
where z_i is a given function, a_<ij> and B_<ij> are technological coefficients. M_<i1> = (a_<22>B_<i1> + a_<21>B<i2>) / (a_<11>a_<22> - a_<12>a_<21>) and M_<i2> = (a_<11>B_<i2> + a_<12>B_<i1>) / (a_<11>a_<22> - a_<12>a_<21>). y_i is a net flow of the product i. γ_i is the delay for the process i.
Then, we investigated the following model with n sectors.
a_<ii>x_i(t) -Σ__<i≠j>a_<ij>x_j(t) - Σ^^n__<j=1>B_<ij> (dx_j (t-γ_j)) / (dt) = z_i(t), (3)
where i = 1, 2, . . . , n.
We published the following book. The Origin of Ecological Economics : The Bioeconomics of Georgescu-Roegen, London : Routledge, 2001.
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Research Products
(2 results)
