Skip to main content
SpringerLink
Log in

Linearized oscillations in population dynamics

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

A linearized oscillation theorem due to Kulenović, Ladas and Meimaridou (1987,Quart. appl. Math. XLV, 155–164) and an extension of it are applied to obtain the oscillation of solutions of several equations which have appeared in population dynamics. They include the logistic equation with several delays, Nicholson's blowflies model as described by Gurney, Blythe and Nisbet (1980,Nature, Lond. 287, 17–21) and the Lasota-Wazewska model of the red blood cell supply in an animal. We also developed a linearized oscillation result for difference equations and applied it to several equations taken from the biological literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Gopalsamy, K. 1986. “Oscillations in a Delay-logistic Equation.”Quart. appl. Math. XLIV, 447–461.

    MathSciNet  Google Scholar 

  • Gurney, W. S. C., S. P. Blythe and R. M. Nisbet. 1980. “Nicholson's Blowflies Revisited.”Nature, Lond. 287, 17–21.

    Article  Google Scholar 

  • Hunt, B. R. and J. A. Yorke. 1984. “When all Solutions of\(x' = - \sum {_{i = 1}^n q} _i (t)x(t - T_i (t))\) Oscillate.”J. diff. Eqns 53, 139–145.

    Article  MATH  MathSciNet  Google Scholar 

  • Kakutani, S. and L. Markus. 1958. “On the Non-linear Difference-differentiual Equation\(\dot Y(t) = \left[ {A - By(t - \tau )} \right]y(t)\).”Contribution to the Theory of Nonlinear. Oscillations, Vol. 4, pp. 1–18. Princeton University Press.

  • Kaplan, J. L. and J. A. Yorke. 1977. “On the Nonlinear Differential Delay Equation\(\dot x(t) = - f(x(t),x(t - 1))\).”J. diff. Eqns. 23, 293–314.

    Article  MATH  MathSciNet  Google Scholar 

  • Kulenović, M. R., G. Ladas and A. Meimaridou. 1987. “On Oscillation of Nonlinear Delay Differential Equations.”Quart. appl. Math. XLV, 155–164.

    Google Scholar 

  • Ladas, G. and I. P. Stavroulakis. 1982. Oscillations Caused by Several Retarded and Advanced Arguments.”J. diff. Eqns 44, 134–152.

    Article  MATH  MathSciNet  Google Scholar 

  • May, R. M. 1975. “Biological Populations Obeying Difference Equations: Stable Points, Stable Cycles and Chaos.”J. theor. Biol. 51, 511–524.

    Article  Google Scholar 

  • — and G. F. Oster. 1976. “Bifurcations and Dynamic Complexity in Simple Ecological Models.”Am. Nat. 110, 537–599.

    Google Scholar 

  • Wright, E. M. 1955. “A Nonlinear Difference-differential Equation.”J. Reine Angew. Math. 194, 66–87.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Rhode Island, 02881, Kingston, RI, USA

    M. R. S. Kulenović & G. Ladas

  2. Department of Mathematics, University of Sarajevo, 71000, Sarajevo, Yugoslavia

    M. R. S. Kulenović

Authors
  1. M. R. S. Kulenović
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Ladas
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kulenović, M.R.S., Ladas, G. Linearized oscillations in population dynamics. Bltn Mathcal Biology 49, 615–627 (1987). https://doi.org/10.1007/BF02460139

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460139

Keywords

Search

Navigation