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Landscape dynamics. To make a crude model of a forest we might introduce states 0 = grass, 1 =…


Landscape dynamics. To make a crude model of a forest we might introduce states 0 = grass, 1 = bushes, 2 = small trees, 3 = large trees, and write down a transition matrix like the following:

Landscape dynamics. To make a crude model of a forest we might introduce states 0 = grass, 1 =...

The idea behind this matrix is that if left undisturbed a grassy area will see bushes grow, then small trees, which of course grow into large trees. However, disturbances such as tree falls or fires can reset the system to state 0. Find the limiting fraction of land in each of the states.