Models which assume a nonlinear relationship between the growth rate and the population size can also generate realistic growth forms. One of the simplest nonlinear models (commonly referred to as the May model) is expressed as
where e is the base of the natural logarithm, r is the intrinsic rate of increase, and K is the carrying capacity of the environment. This model assumes the relationship between r and N is nonlinear and the growth form exhibited by this model depends on the value of r, K, and the initial value of N. The growth forms of this model are analogous to that of eqn . The model will reach a stable equilibrium at Kif 1.99 > r > 0, stable limit cycles (with 2, 4, 8, or 16 endpoints) if 2.692 > r > 2.0, or become chaotic (nonrepeatable pattern) if r> 2.693.
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