       Re: question RE: difference equations

• To: mathgroup at smc.vnet.net
• Subject: [mg26086] Re: [mg26066] question RE: difference equations
• From: Ken Levasseur <Kenneth_Levasseur at uml.edu>
• Date: Tue, 28 Nov 2000 01:55:32 -0500 (EST)
• References: <200011220655.BAA19960@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```John:

Since the system you've described is linear, I'd turn it into a single matrix
equation.   Then you have access to all of the matrix algebra functions to
analyze the system.  For example, the eigenvalues of A in the equation X[t]=A
X[t-1] tell you a lot about the stability of the system.

Ken Levasseur
UMass Lowell

John McArthur wrote:

> I am a new Mathematica user so apologize for the basic nature of my
> question:
>
> I want to set up a system of simultaneous difference equations but am
> having trouble with the syntax. Essentially I would like to map the growth
> of a system as follows:
>
> y1(t)=y1(t-1) + a*y2(t-1) + b*y3(t-1)... + xx*yn(t-1)
> y2(t)=y2(t-1) + c*y1(t-1) + d*y3(t-1)... + yy*yn(t-1)
> ...
> yn(t)=yn(t-1) + x*y1(t-1) + z*y2(t-1)... + zz*y[n-1](t-1)
>
> I know how to set up a univariate recursive equation, but am not clear on
> how to set up a multivariate form. My most common error message is one of
> "recursion limit reached."  Any suggestions (and possibly advice
> on the simplest way to set up a system like the one above) would be
> greatly appreciated.
>
> Many thanks,
> John McArthur

```

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