Journal of Mathematical Biology

, Volume 3, Issue 2, pp 197–201 | Cite as

On the stability of the stationary state of a population growth equation with time-lag

  • K. P. Hadeler
Article

Summary

If in the Verhulst equation for population growth the reproduction factor depends on the history then the equilibrium may become unstable and oscillations and even non-constant periodic solutions may occur. It is shown that the equilibrium is unstable if the reproduction factor at time t is, up to a sufficiently large factor, an arbitrary average of the population densities in the interval (t−2, t−1].

Keywords

Population Density Population Growth Stochastic Process Stationary State Periodic Solution 
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References

  1. [1]
    Walther, H. O.: Existence of a non-constant periodic solution of a non-linear autonomous functional differential equation representing the growth of a single species population. J. Math. Biol. 1, 227–240 (1975).Google Scholar
  2. [2]
    Walther, H. O.: On a transcendental equation in the stability analysis of a population growth model. J. of Math. Biol. 3, 187–195 (1976).Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • K. P. Hadeler
    • 1
  1. 1.Lehrstuhl für BiomathematikUniversität TübingenTübingenFederal Republic of Germany

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