zbMATH — the first resource for mathematics

Permanence for Nicholson-type delay systems with nonlinear density-dependent mortality terms. (English) Zbl 1232.34109
Sufficient conditions are obtained for permanence of the following system \[ x^{'}_1(t)=-D_{11}(t,x_1(t))+D_{12}(t,x_2(t)) +c_1(t)x_1(t-\tau_1(t))e^{-\gamma_1(t)x_1(t-\tau_1(t))}, \] \[ x^{'}_2(t)=-D_{22}(t,x_2(t))+D_{21}(t,x_1(t)) +c_2(t)x_2(t-\tau_2(t))e^{-\gamma_2(t)x_2(t-\tau_2(t))}. \]

34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
34K25 Asymptotic theory of functional-differential equations
Full Text: DOI
[1] Nicholson, A., An outline of the dynamics of animal populations, Australian journal of zoology, 2, 9-65, (1954)
[2] Gurney, W.; Blythe, S.; Nisbet, R., Nicholson’s blowflies revisited, Nature, 287, 17-21, (1980)
[3] Nisbet, R.; Gurney, W., Modelling fluctuating populations, (1982), John Wiley and Sons NY · Zbl 0593.92013
[4] Berezansky, L.; Idels, L.; Troib, L., Global dynamics of Nicholson-type delay systems with applications, Nonlinear analysis: real world applications, 12, 1, 436-445, (2011) · Zbl 1208.34120
[5] Berezansky, L.; Braverman, E.; Idels, L., Nicholson’s blowflies differential equations revisited: main results and open problems, Applied mathematical modelling, 34, 1405-1417, (2010) · Zbl 1193.34149
[6] B. Liu, Permanence for a delayed Nicholson’s blowflies model with a nonlinear density-dependent mortality term, Annales Polonici Mathematici, 2011 (APM 2204, in press). · Zbl 1242.34145
[7] Smith, H.L., ()
[8] Hale, J.K.; Verduyn Lunel, S.M., Introduction to functional differential equations, (1993), Springer-Verlag New York · Zbl 0787.34002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.