[OPE-L:6603] [OPE-L:64] nonlinear difference equation with variable coefficients

Patrick L. Mason (Patrick.L.Mason.20@nd.edu)
Sat, 25 Jul 1998 14:40:50 -0500

Dear OPE-Lers:

I'm trying to obtain help deriving the dynamics, stability, and equilibrium
of a 3x3 system of difference

equations. One version of the model has constant coefficients and the other
has variable coefficients. Here's

the model.

W(t) = c(I1(t-1),I0(t-1))*X(t)

I0(t) = b0 + b1*W(t) + b2*H(I0(t-1)) + b3*K(I1(t-1))

I1(t) = a0 - a1*W(t) + a2*H(I1(t-1)) + a3*K(I0(t-1))

a0, a1, a2, a3, b0, b1, b2, b3, and c are coefficients. H and K are
functions. W, X, I0, and I1 are

variables. In the more complex version of the model these coefficients are
variable. That is,

b1 = b1(I0(t-1),I1(t-1)) > 0 and a1 = a1(I1(t-1),I0(t-1)) > 0.

Is there a standard reference to models of this type? If so, is the
reference accessible to an economist (me)?

Any help you can provide will greatly appreciated.

Thanks, Patrick L. Mason