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Equilibrium Values in Systems of Difference Equations

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Consider the interaction of two species whose populations after n years are represented by the numbers xn and yn. Consider the following model:

xn+1 = 0.8xn + 0.002xnyn

yn+1 = 0.9yn + 0.001xnyn

x0 = 50

y0 = 100

Iterate the system. Can the two species coexist? Is there an equilibrium value?

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Iterating the two difference equations in Excel shows that the two species cannot ...

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The expert examines equilibrium values in systems of difference equations.