Chaos in Nonlinear Dynamics and the Logistic Substitution Model

Keepin, W. (1982). Chaos in Nonlinear Dynamics and the Logistic Substitution Model. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-82-086

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Abstract

A rekindled appreciation of an old cliche has touched off a flurry of activity in the field of nonlinear dynamics lately. The truism that nonlinearities often lead to wild and exotic behavior has been known for a long time, but only recently has it been studied carefully, and the discoveries are startling and profound. The simplest equation illuminating these features is the logistic equation (in discrete form), which has a long history of application to growth phenomena in biology and population dynamics. This equation is also the basis for the logistic substitution model developed at IIASA by Cesare Marchetti and Nebojsa Nakicenovic. This model is a highly effective tool for modeling the dynamics of economic market substitution, and has been extensively applied to primary energy markets.

This Working Paper begins with a brief review of the recent developments in nonlinear dynamics, followed by a study of the implications that these phenomena have for the logistic substitution model. The key finding is that only highly unrealistic parameter values can induce chaotic behavior in this model.

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