I have no programming experience and trying to get mathematica to do what I need it to do is frustrating. I have the following functions that I need to iterate. For notational purposes, k[t+1] is the value of K in the next period. w is a parameter.(adsbygoogle = window.adsbygoogle || []).push({});

k[t+1] = -x[t] - y[t] + w

x[t+1] = k[t]*sqrt(y[t]/(-y[t] + w)) - y[t]

y[t+1] = k[t]*sqrt(x[t]/(-x[t] + w)) - x[t]

As I care more about the behavior of x and y, this system can be reduced to:

x[t+2] = (-x[t]-y[t]+w)*sqrt(y[t+1]/(-y[t+1] + w)) - y[t+1]

y[t+2] = (-x[t]-y[t]+w)*sqrt(x[t+1]/(-x[t+1] + w)) - x[t+1]

I have already found for what w the system becomes unstable by taking the Jacobian of the 3-system and seeing where it exceeds unity in absolute value. Now I just want to iterate the system and get some pretty graphs.

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# Iterative map in mathematica

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