Studies on the stability of a Leontief dynamic model with delays

首先,我们investigatd以下modela_ < 11 > x_1 (t)——现代< 12 > x_2 (t) - B_ < 11 > (dx_1 (t -γ_1))/ (dt)——B_ < 12 > (dx_2 (t -γ_2))/ (dt) = z_1 (t)(1)现代< 12 > x_1 (t) +现代< 22 > x_2 (t) - B_ < 21 > (dx_1 (t -γ_1))/ (dt)——B_ < 22 > (dx_2 (t -γ_2))/ (dt) = z_2 (t), (2) z_i是一个给定的函数,现代< ij >和B_ < ij >技术系数。M_ < i1 > =(现代< 22 > B_ < i1 > +现代< 21 > B < i2 >) /(现代< 11 >现代< 22 >——现代< 12 >现代< 21 >)和M_ < i2 > =(现代< 11 > B_ < i2 > +现代< 12 > B_ < i1 >) /(现代< 11 >现代< 22 >——现代< 12 >现代< 21 >)。y_i是产品i的净流量，γ_i是过程i的延迟。然后，我们研究了有n个扇区的模型。现代<二> x_i (t) -Σ__ <我≠j >现代< ij > x_j (t) -Σ^ ^ n__ < j = 1 > B_ < ij > (dx_j (t -γ_j)) / (dt) = z_i (t),(3) = 1, 2,。我们出版了下面的书。生态经济学的起源：乔治斯库-罗根的生物经济学，伦敦：劳特利奇出版社，2001。

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.