Studies on the stability of a Leontief dynamic model with delays

首先，我们研究了如下模型a_&lt；11&gt；x_1(T)-a_&lt；12&gt；x_2(T)-B_&lt；11&gt；(dx_1(t-γ_1))/(Dt)-B_&lt；12&gt；(dx_2(t-γ_2))/(Dt)=z_1(T)，(1)-a_&lt；12&gt；22&gt；x_2(T)-B_&lt；21&gt；(dx_1(t-γ_1))/(Dt)-B_&lt；22&gt；(dx_2(t-γ_2))/(Dt)=z_2(T)，(2)其中z_i是给定函数，a_&lt；ij&gt；和B_&lt；ij&gt；是工艺系数。M_&lt；i1&gt；=(a_&lt；22&gt；B_&lt；i1&gt；a_&lt；b&lt；i2&gt；)/(a_&lt；11&gt；a_&lt；22&gt；-a_&lt；12&gt；a_&lt；21&gt；)和M_&lt；i2&gt；=(a_&lt；11&gt；B_&lt；i2&gt；a_&lt；12&gt；B_&lt；i1&>)/(a_&lt；11&gt；a_&lt；22&gt；-a_&lt；12&gt；a_&lt；21&gt；)。Y_i是乘积i的净流，γ_i是过程i的延迟。然后，我们研究了具有n个扇区的如下模型：a_&lt；ii&gt；x_i(T)-Σ__&lt；i≠j&gt；a_&lt；ij&gt；x_j(T)-Σ^n_&lt；j=1&gt；B_&lt；ij&gt；(dx_j(t-γ_j))/(Dt)=z_i(T)，(3)其中i=1，2，.。。我们出版了下面这本书。《生态经济学的起源：乔治埃斯库-罗根的生物经济学》，伦敦：鲁特利奇出版社，2001年版。

First, we investigatd the following modela_<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.