Biological populations obeying difference equations: stable points, stable cycles, and chaos.

@article{May1975BiologicalPO,
  title={Biological populations obeying difference equations: stable points, stable cycles, and chaos.},
  author={Robert M. May},
  journal={Journal of theoretical biology},
  year={1975},
  volume={51 2},
  pages={511-24}
}
For biological populations with nonoverlapping generations, population growth takes place in discrete time steps and is described by difference equations. Some of the simplest such nonlinear difference equations can exhibit a remarkrible spectrum of dynamical behavior, from stable equilibrium points, to stable cyclic oscillations between two population points, to stable cycles with four points, then eight, 16, etc., points, through to a chaotic regime in which (depending on the initial… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-9 of 9 references

Tellus 16, 1

E. N. LORENZ
MACFADYEN, A. (1963). Animal Ecology. London: Pitman. • 1964
View 4 Excerpts
Highly Influenced

Am

MAY R.M.R.M. MAY
Nat. 107, • 1972
View 5 Excerpts
Highly Influenced

An Introduction to Mathematical Ecolonv

C. PIELOU.E.
New York: Wiley. Scmo; F. M. ‘& L&NE, F. (1974). (In press.) • 1969
View 2 Excerpts
Highly Influenced

Insect Population Ecology, pp. 20-25

G. C. VARLEY, G. R. GRADWELL, M. P. HASSELL
Oxford: BIackwells. WILLIAMSON, M • 1973

Stability and Complexity in Model Ecosystems

IEEE Transactions on Systems, Man, and Cybernetics • 1973

Ecology: The Experimental Analysis of Distribution and Abundance

J. R. KREBS
New York: Harper and Row. LESLIE, P. H. (1957). Biometrika 44, 314. • 1972
View 2 Excerpts

Mathematical Ideas in Biology

J. MAYNARD Sm
Cambridge: Cambridge University Press. MAYNARD SMITH, J. (1974). Models in Ecology, p. 53. Cambridge: Cambridge University Press. PENNYCUIK, C. J., COMPTON, R. M. & BECKINGHAM, L. (1968). J. theor. Biol. 18, 316. • 1968
View 1 Excerpt

Nature, Lond

L. M. COOK
207, 316. • 1965
View 2 Excerpts

Biometrika 39, 346

J. F. SKELLAM
USHER, M. B. (1972). In Mathematical Models in Ecology (J. N. R. Jeffers, ed.), pp. 29-60. Oxford : Blackwells. USA, S. (1967). Res. Pop. Ecol. 9, 1. VAN DER VAART, H. R. (1973). Bcdl. math. Biophys. 35, 19.5. • 1952
View 2 Excerpts

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