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