Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On a periodic delay population model

Authors: B. S. Lalli and B. G. Zhang
Journal: Quart. Appl. Math. 52 (1994), 35-42
MSC: Primary 92D25; Secondary 34K20
DOI: https://doi.org/10.1090/qam/1262316
MathSciNet review: MR1262316
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Abstract | References | Similar Articles | Additional Information

Abstract: The existence of a positive periodic solution for

$\displaystyle N'(t) = N(t)\left[ {a(t) + b(t)N(t - m\omega ) - c(t){N^2}(t - m\omega )} \right]$

is established. Sufficient conditions are given for the periodic solution to be globally attractive.

References [Enhancements On Off] (What's this?)

  • [1] W. C. Allee, Animal aggregations, Quart. Reviews of Biology 2, 367-398 (1927)
  • [2] I. Barbalat, Systèmes d'équations différentielles des oscillations non linéaires, Rev. Math. Pures Appl. 4, 267-270 (1959)
  • [3] W. J. Cunningham, A nonlinear differential-difference equation of growth, Proc. Nat. Acad. Sci. U.S.A. 40, 708-713 (1954)
  • [4] K. Gopalsamy and G. Ladas, On the oscillation and asymptotic behavior of $ N'\left( t \right) = \\ N\left( t \right)\left[ {a + bN\left( t - \tau \right) - c{N^2}\left( t - \tau \right)} \right]$, Quart. Appl. Math. XLVIII, 433-440 (1990)
  • [5] K. Gopalsamy, M. R. S. Kulenovic, and G. Ladas, Environmental periodicity and time delay in a ``food limited'' population model, J. Math. Anal. Appl. 107, 545-555 (1990)
  • [6] G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation Theory of Differential Equations With Deviating Arguments, Marcel Dekker, New York, 1987
  • [7] A. J. Nicholson, The balance of animal population, J. Animal Ecology 2, 132-178 (1933)
  • [8] E. R. Pianka, Evolutionary Ecology, Harper and Row, New York, 1974
  • [9] B. G. Zhang and K. Gopalsamy, Global attractivity and oscillations in a periodic delay logistic equation, J. Math. Anal. Appl. 150, 270-283 (1990)

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DOI: https://doi.org/10.1090/qam/1262316
Article copyright: © Copyright 1994 American Mathematical Society

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