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Zbl 0614.92015
Rosen, Gerald
Time delays produced by essential nonlinearity in population growth models. (English)
[J] Bull. Math. Biol. 49, 253-255 (1987). ISSN 0092-8240; ISSN 1522-9602/e

It is pointed out that the asymptotic general solution to the $\theta$- model equation for a periodic carrying capacity K(t) and $t\succcurlyeq r\sp{-1}$ is identical in form to the generalized logistic equation solution with a built-in developmental time delay $\tau (\preccurlyeq r\sp{-1})$ and associated parameter ranges of primary biological interest. In the case of the $\theta$-model equation, the time delay is a purely dynamical consequence of the nonlinear form featured by the population growth rate.

MSC 2000:: *92D25 Population dynamics
34A45 Theoretical approximation of solutions of ODE
34A34 Nonlinear ODE and systems, general

Keywords: generalized Verhulst growth; theta model equation; asymptotic general solution; periodic carrying capacity; generalized logistic equation solution; developmental time delay; population growth rate

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