On the oscillation and asymptotic behavior of $\dot N(t)=N(t)[a+bN(t-\tau )-cN^2(t-\tau )]$
Authors:
K. Gopalsamy and G. Ladas
Journal:
Quart. Appl. Math. 48 (1990), 433-440
MSC:
Primary 34K15; Secondary 34K20, 92D25
DOI:
https://doi.org/10.1090/qam/1074958
MathSciNet review:
MR1074958
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We obtained sufficient conditions for all positive solutions of the equation in the title to oscillate about the positive equilibrium ${N^ * }$ . We also found sufficient conditions for the global attractivity of ${N^ * }$.
W. C. Allee, Animal aggregations, Quart. Review of Biology 2, 367–398 (1927)
W. C. Allee, Animal aggregations: A study in general sociology, Chicago University Press, Chicago, 1931
- I. Barbălat, Systèmes d’équations différentielles des oscillations non linéaires, Com. Acad. R. P. Romîne 9 (1959), 779–782 (Romanian, with French and Russian summaries). MR 111895
M. E. Gilpin and F. J. Ayala, Global models of growth and competition, Proc. Nat. Acad. Sci. 70, 3590–3593 (1973)
- K. Gopalsamy, A delay induced bifurcation to oscillations, J. Math. Phys. Sci. 16 (1982), no. 5, 469–488. MR 700794
G. E. Hutchinson, Circular causal systems in ecology, Ann. N.Y. Acad. Sci. 50, 221–246 (1948)
- Gerasimos Ladas, Sharp conditions for oscillations caused by delays, Applicable Anal. 9 (1979), no. 2, 93–98. MR 539534, DOI https://doi.org/10.1080/00036817908839256
K. E. F. Watt, Ecology and Resource Management, McGraw Hill, New York, 1968
W. C. Allee, Animal aggregations, Quart. Review of Biology 2, 367–398 (1927)
W. C. Allee, Animal aggregations: A study in general sociology, Chicago University Press, Chicago, 1931
I. Barbalat, Systemes d’equations differentielles d’oscillations nonlineaires, Rev. Roumaine Math. Pures Appl. 4, 267–270 (1959)
M. E. Gilpin and F. J. Ayala, Global models of growth and competition, Proc. Nat. Acad. Sci. 70, 3590–3593 (1973)
K. Gopalsamy, A delay induced bifurcation to oscillations, J. Math. Phys. Sci. 16, 469–488 (1982)
G. E. Hutchinson, Circular causal systems in ecology, Ann. N.Y. Acad. Sci. 50, 221–246 (1948)
G. Ladas, Sharp conditions for oscillations caused by delays, Applicable Analysis 9, 93–98
K. E. F. Watt, Ecology and Resource Management, McGraw Hill, New York, 1968
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
34K15,
34K20,
92D25
Retrieve articles in all journals
with MSC:
34K15,
34K20,
92D25
Additional Information
Article copyright:
© Copyright 1990
American Mathematical Society
