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On the stability for a population growth equation with time delay

Published online by Cambridge University Press:  14 November 2011

Jitsuro Sugie
Jitsuro Sugie
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan
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Synopsis

In this paper we give a sufficient condition which guarantees that the zero solution of a population growth equation is uniformly stable.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 1-2 , 1992 , pp. 179 - 184
Copyright
Copyright © Royal Society of Edinburgh 1992

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References

1Cunningham, W. J.. A nonlinear differential-difference equation of growth. Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 708–713.CrossRefGoogle ScholarPubMed
2Grafton, R. B.. A periodicity theorem for autonomous functional differential equations. J. Differential Equations 6 (1969), 87–109.CrossRefGoogle Scholar
3Hutchinson, G. E.. Circular causal systems in ecology. Ann. New York Acad. Sci. 50 (1948), 221–246.CrossRefGoogle ScholarPubMed
4Jones, G. S.. The existence of periodic solutions of f'(x) = -αf(x - 1)[1 + f(x)]. J. Math. Anal. Appl. 5 (1962), 435–450.CrossRefGoogle Scholar
5Kakutani, S. and Markus, L.. On the nonlinear difference-differential equation y'(t) = [A – By(t – Ʈ)]y(t). Contrs. Theory Nonlinear Oscilations 4 (1958), 1–18.Google Scholar
6Kaplan, J. L. and Yorke, J. A.. On the stability of a periodic solution of a differential delay equation. SIAM J. Math. Anal. 6 (1975), 268–282.Google Scholar
7May, R. M.. Stability and Complexity in Model Ecosystems (Princeton: Princeton University Press, 1973).Google ScholarPubMed
8Nussbaum, R. D.. Periodic solutions of some nonlinear autonomous functional differential equations II. J. Differential Equations 14 (1973), 360–394.CrossRefGoogle Scholar
9Wright, E. M.. A non-linear difference-differential equation. J. Reine Angew. Math. 194 (1955), 66–87.CrossRefGoogle Scholar