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Global attractivity in Nicholson’s blowflies. (English) Zbl 0867.34042

The author studies the delay differential equation

N ' (t)=-δN(t)+pN(t-τ)exp(-aN(t-τ)),t0,

used in describing the dynamics of Nicholson’s blowflies. When p>δ, he establishes sufficient conditions for the global attractivity of the nontrivial equilibrium.

MSC:
34D45Attractors
34K20Stability theory of functional-differential equations
References:
[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.
[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.