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Stable steady state of some population models

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Abstract

Applying an analytical method and several limiting equations arguments, some sufficient conditions are provided for the existence of a unique positive equilibriumK for the delay differential equationx=−γx+D(x t ), which is the general form of many population models. The results are concerned with the global attractivity, uniform stability, and uniform asymptotic stability ofK. Application of the results to some known population models, which shows the effectiveness of the methods applied here, is also presented.

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References

  • Arino, O., and Kimmel, M. (1986). Stability analysis of models of cell production systems.Math. Model. 7, 1269–1300.

    Google Scholar 

  • Glass, L., Beuter, A., and Larocque, D. (1988). Time delays, oscillations, and chaos in physiological control systems.Math. Biosci. 90, 111–125.

    Google Scholar 

  • Gopalsamy, K., Kulenović, M. R. S., and Ladas, G. (1990). Oscillations and global attractivity in models of haematopoiesis.J. Dynam. Diff. Eq. 2, 117–132.

    Google Scholar 

  • Gurney, W. S. C., Blythe, S. P., and Nisbet, R. M. (1980). Nicholson's blowflies revisited.Nature 287, 17–21.

    Google Scholar 

  • Karakostas, G. (1982). Causal operators and topological dynamics.Ann. Mat. Pura Appl. 131, 1–27.

    Google Scholar 

  • Kulenović, M. R. S., and Ladas, G. (1987). Linearized oscillations in the population dynamics.Bull. Math. Biol. 49, 615–627.

    Google Scholar 

  • Kulenović, M. R. S., Ladas, G., and Sficas, Y. G. (1989). Global attractivity in population dynamics.Comput. Math. Appl. 18, 825–925.

    Google Scholar 

  • Kulenović, M. R. S., Ladas, G., and Sficas, Y. G. (1991). Global attractivity in Nicholson's blowflies.Applicable Anal. (in press).

  • Mackey, M. C., and Glass, L. (1977). Oscillation and chaos in physiological control systems.Science 197, 287–289.

    Google Scholar 

  • Mallet-Paret, J., and Nussbaum, R. D. (1986). Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation.Ann. Mat. Pura Appl. 145, 33–128.

    Google Scholar 

  • Sell, G. R. (1971).Topological Dynamics and Ordinary Differential Equations, Van Nostrand-Reinhold, London.

    Google Scholar 

  • Sibirsky, K. R. (1975).Introduction to Topological Dynamics, Noordhoff International, Leyden.

    Google Scholar 

  • Wazewska-Czyzewska, M., and Lasota, A. (1976). Mathematical problems of the red-blood cell system (in Polish),Ann. Polish Math. Soc. Ser. III Appl. Math. 6, 23–40.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Ioannina, P.O. Box 1186, 45110, Ioannina, Greece

    G. Karakostas, Ch. G. Philos & Y. G. Sficas

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  1. G. Karakostas
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  2. Ch. G. Philos
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  3. Y. G. Sficas
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Karakostas, G., Philos, C.G. & Sficas, Y.G. Stable steady state of some population models. J Dyn Diff Equat 4, 161–190 (1992). https://doi.org/10.1007/BF01048159

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