Simple mathematical models with very complicated dynamics
- 10 June 1976
- journal article
- review article
- Published by Springer Nature in Nature
- Vol. 261 (5560) , 459-467
- https://doi.org/10.1038/261459a0
Abstract
First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamic behavior, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. An interpretive review of them is presented.This publication has 28 references indexed in Scilit:
- Biological populations obeying difference equations: Stable points, stable cycles, and chaosPublished by Elsevier ,2004
- Cascading Bifurcations: The Mathematics of ChaosScience, 1975
- Density-Dependence in Single-Species PopulationsJournal of Animal Ecology, 1975
- On Relationships Among Various Types of Population ModelsThe American Naturalist, 1973
- Oscillation in the Simple Logistic Growth ModelNature, 1965
- Stock and RecruitmentJournal of the Fisheries Research Board of Canada, 1954
- The Nonlinear Accelerator and the Persistence of Business CyclesEconometrica, 1951
- Zur Steuerreform der OstzoneJuristische Rundschau, 1950
- On the Distribution of Values of Sums of the Type Σf(2 k t)Annals of Mathematics, 1946
- THE CONVERGENCE OF SEQUENCES DEFINED BY QUADRATIC RECURRENCE-FORMULAEThe Quarterly Journal of Mathematics, 1936