Published in Nature, Vol. 261, p.459, June 10 1976.

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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 dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of. the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

Table of Contents

INTRODUCTION

FIRST-ORDER DIFFERENCE EQUATIONS

DYNAMIC PROPERTIES OF EQUATION (1)

FINE STRUCTURE OF THE CHAOTIC REGIME

PRACTICAL PROBLEMS

MATHEMATICAL CURIOSITIES

APPLICATIONS

RELATED PHENOMENA IN HIGHER DIMENSIONS

CONCLUSION

REFERENCES

For a Postscript version of the article, click here.

* King's College Research Centre, Cambridge CB2 1ST; on leave front Biology Department, Princeton University, Princeton 08540.