Bifurcation

Chaos is also known in relation to bifurcation. The following equation yields bifurcation:

where r is the growth rate per capita, t is the time, N the number of organisms, and Kthe carrying capacity. When r is above 2, the equation gives two stable fixed points; when above 2.6, four stable fixed points; when above

2.75, eight stable fixed points; and through successive bifurcations, an infinite hierarchy of stable cycles of the period 2n arises.

Chaos is rare in ecological systems, but a few examples show that chaos may occur. The best known example is the lemming population, where density (number per hectare) may fluctuate between two bifurcation values.

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