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Global attractivity in Nicholson’s blowflies. (English) Zbl 0867.34042
The author studies the delay differential equation $$N'(t)=-\delta N(t)+pN(t-\tau)\exp(-aN(t-\tau)),\quad t\ge0,$$ used in describing the dynamics of Nicholson’s blowflies. When $p>\delta$, he establishes sufficient conditions for the global attractivity of the nontrivial equilibrium.

34K20Stability theory of functional-differential equations
Full Text: DOI
[1] Kulenovic, M. R. S., Ladas, G. and Sficas, Y. G., Global attractivity in Nicholson’s blowflies,Applicable Analysis,43 (1992), 109--124. · Zbl 0754.34078 · doi:10.1080/00036819208840055
[2] So, W. H. and Yu, J. S., Global attractivity and Uniform Persistence in Nicholson’s blowflies,Differential Equations and Dynamical System,2:1 (1994), 11--18. · Zbl 0869.34056
[3] Gurney, W. S. C, Blythe, S. P. and Nisbet, R. M., Nicholson’s blowflies revisited,Nature,287 (1980), 17--21. · doi:10.1038/287017a0
[4] Karakostas, G., Phios, Ch. G. and Sficas, Y. G., Stable steady state of some population models,J. Dynamics and Diff. Eqs. 4 (1992), 161--190. · Zbl 0744.34071 · doi:10.1007/BF01048159
[5] Györe, I. and Ladas, G., Oscillation theory of delay differential equations with applications, Clarendon Press, Oxford, 1991. · Zbl 0780.34048