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Existence of positive periodic solutions for a generalized Nicholson’s blowflies model. (English) Zbl 1147.92031
Summary: By using the Krasnoselskii cone fixed point theorem, we obtain a sufficient condition as well as a necessary condition for the existence of positive periodic solutions of the following generalized {\it A. J. Nicholson}’s [An outline of the dynamics of animal populations. Aust. J. Zool. 2, 9--25 (1954)] blowflies model: $$x'(t)=- \delta(t)x(t)+ \sum_{i=1}^m p_i(t)x(t-\tau_i(t)) e^{-q_i(t)x(t-\tau_i(t))}, \quad t\ge 0.$$ In the degenerate case, i.e., where the coefficients and delays of the above equation are all constants, a sufficient and necessary condition for the existence of positive periodic solutions is obtained. Our results are completely new, and generalize and improve some results from the literature.

92D25Population dynamics (general)
34K13Periodic solutions of functional differential equations
34K60Qualitative investigation and simulation of models
Full Text: DOI
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