On the stability of the stationary state of a population growth equation with time-lag
- 1 January 1976
- journal article
- research article
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 3 (2) , 197-201
- https://doi.org/10.1007/bf00276206
Abstract
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
This publication has 2 references indexed in Scilit:
- On a transcendental equation in the stability analysis of a population growth modelJournal of Mathematical Biology, 1976
- Existence of a non-constant periodic solution of a non-linear autonomous functional differential equation representing the growth of a single species populationJournal of Mathematical Biology, 1975