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Time delays produced by essential nonlinearity in population growth models. (English) Zbl 0614.92015

It is pointed out that the asymptotic general solution to the \(\theta\)- model equation for a periodic carrying capacity K(t) and \(t\succcurlyeq r^{-1}\) is identical in form to the generalized logistic equation solution with a built-in developmental time delay \(\tau (\preccurlyeq r^{-1})\) 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:

92D25 Population dynamics (general)
34A45 Theoretical approximation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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