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
Full-text PDF Free Access
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Abstract: The existence of a positive periodic solution for \[ N’(t) = N(t)\left [ {a(t) + b(t)N(t - m\omega ) - c(t){N^2}(t - m\omega )} \right ]\] is established. Sufficient conditions are given for the periodic solution to be globally attractive.
W. C. Allee, Animal aggregations, Quart. Reviews of Biology 2, 367–398 (1927)
I. Barbǎlat, Systèmes d’équations différentielles des oscillations non linéaires, Rev. Math. Pures Appl. 4, 267–270 (1959)
W. J. Cunningham, A nonlinear differential-difference equation of growth, Proc. Nat. Acad. Sci. U.S.A. 40, 708–713 (1954)
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)
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)
G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation Theory of Differential Equations With Deviating Arguments, Marcel Dekker, New York, 1987
A. J. Nicholson, The balance of animal population, J. Animal Ecology 2, 132–178 (1933)
E. R. Pianka, Evolutionary Ecology, Harper and Row, New York, 1974
B. G. Zhang and K. Gopalsamy, Global attractivity and oscillations in a periodic delay logistic equation, J. Math. Anal. Appl. 150, 270–283 (1990)
W. C. Allee, Animal aggregations, Quart. Reviews of Biology 2, 367–398 (1927)
I. Barbǎlat, Systèmes d’équations différentielles des oscillations non linéaires, Rev. Math. Pures Appl. 4, 267–270 (1959)
W. J. Cunningham, A nonlinear differential-difference equation of growth, Proc. Nat. Acad. Sci. U.S.A. 40, 708–713 (1954)
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)
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)
G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation Theory of Differential Equations With Deviating Arguments, Marcel Dekker, New York, 1987
A. J. Nicholson, The balance of animal population, J. Animal Ecology 2, 132–178 (1933)
E. R. Pianka, Evolutionary Ecology, Harper and Row, New York, 1974
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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Article copyright:
© Copyright 1994
American Mathematical Society
