Chaos in Nonlinear Dynamics and the Logistic Substitution Model

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

A Critical Appraisal of the IIASA Energy Scenarios

This paper presents some disturbing findings about one aspect of a major scientific study of the world's energy system. The final report of the seven-year study was published in 1981, entitled "Energy in a "Finite World." Although the study claims to provide an objective, factual analysis for political decision making, some of the major conclusions are not scientifically justified. Principal results include detailed projections of the world's energy supply systems for the coming half-century. These were produced from an apparently sophisticated set of iterative computer models. However, the models are found to be largely trivial, because their final outputs are nearly identical to their inputs, which are arbitrary, unsubstantiated assumptions. Furthermore, despite claims of robustness, the energy supply projections are found to be highly sensitive to minor variations in data that are well known to be uncertain. The sizable contribution from the nuclear fast breeder reactor (FBR), is due to a 2% cost advantage that is introduced 25 years from now. Since future energy costs are highly uncertain, cost-minimization linear programming models are unsuitable for describing robust energy supply futures. In addition to these analytic findings, some aspects of the work are improperly presented in the published documentation. In one case, the important role of the FBR is traced to undocumented input data. Frequent statements that the computer models formed an iterative loop are contradicted elsewhere. Preliminary work that revealed serious difficulties with robustness is not cited, and standard sensitivity tests are not included. Nevertheless, several "robust" conclusions have been drawn from the projections and widely publicized. One of these implies that nuclear power plants must be built at the average rate of one plant every few days for the next 50 years. The overall conclusion in this paper is that the energy supply projections are opinion, rather than credible scientific analysis, and they therefore cannot be relied upon by policy makers seeking a genuine understanding of the energy choices for tomorrow

A technical appraisal of the IIASA energy scenarios

Several shortcomings in a major study of the world's energy system are described. The study, entitled Energy in a Finite World, resulted in widely publicized conclusions and urgent policy recommendations that were derived from detailed projections of the global energy future. A set of computer models was used to produce these projections, which are analyzed here in two ways. First, treating the models as a black box, it is shown that several principal results are effectively prescribed informally in input data that pass through the models unchanged. Second, despite claims of robustness, detailed sensitivity analysis shows that the energy supply projections are highly sensitive to perturbations in various input data. Early work that revealed this problem is not cited, and standard sensitivity tests are not provided in the study. Thus, despite the appearance of analytical rigor, the study's conclusions are evidently based on opinions rather than objective robust analysis