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Catastrophes in Nature and Society: Mathematical Modeling of Complex Systems

Khlebopros, Rem G., Okhonin, Viktor A. and Fet, Abram I.
World Scientific Publishing: London, 2006
ISBN 9812569170 (pb)

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Reviewed by Jos Timmermans
Dutch Research Institute For Transitions (DRIFT), Erasmus University Rotterdam

Cover of book At first site Khlebopros, Okhonin and Fet seem to show up as one trick ponies, analyzing phase portraits from cover to cover in their book requiring nothing more than paper and pencil to make their point. However, while developing their argument they extend the analytical strength of their approach with concepts like reflection from bi-sector and shifting phase curves in order to derive the characteristics of repeated and continuous system disturbances from a single event. The last method is reminiscent of the convolution method applied in linear systems. The authors cordially remind us of the fact that this method is first published in this book and I therefore strongly advise them to get it published in a proper peer reviewed scientific journal.

Linear systems, however, are certainly not the systems Khlebopros et al. are looking at. In fact, and that is the second way the authors develop themselves from one trick ponies into conspicuous omnivores, by the sheer number and diversity of applications in their book the authors show that their approach, or if you like their way of thinking, can be applied in relation to virtually every current policy issue. In the meantime leaving the reader/practitioner with the uncomfortable feeling of having used the wrong hammer for virtually every nail encountered in his or her professional career up to now. Fortunate they supply a promising alternative; a paper, pencil, brain power and data driven approach, especially amenable to practitioners.

Let me now first turn to explaining what Khlebopros et al. actually do by spinning out a convincing example from the beginning of their book concerning salmon stock management in Russia's Far East, where salmon, instead of obeying the established 12 miles catch zones, is easily lured into the nets of Japanese fishermen frequenting the border of the 12 miles zone, at the foresight of becoming a Sashimi. The suggestion of ichthyologist to extend the Russian zone of catch from 12 to 24 miles to counteract this practice and increase the Russian salmon yield in practice resulted in a decline in the catch to increase only one or more decades later. Khlebopros et al. present an empirical phase portrait model of salmon catch before and after the increase of the fishing zone and use this model to explain how the salmon population, instead of passing to a new equilibrium state with a greater equilibrium stock, first moves through an extended period with lower stocks.

For the remainder of this review I like to focus on two subjects. First, I want to consider the application of the Khlebopros pencil and paper methods to the avail of our computer focused community, and second I want to address the possibility of extending the pencil and paper approaches to include multi dimensional problems exactly by using these devices. Concerning the first subject, the methods of Khlebopros et al. largely revolve around phase portraits based on empirical data from these systems and characterizing their stability or explaining their evolution. Without the hassle of uncomfortable field work measuring mistakes and uncertainties, such data and thus phase portraits can be obtained form (social) simulation models allowing their output to be reduced, characterized and analyzed in more concise, general and abstract way. In short, build an ABM of the salmon stock, get out the required phase portraits instead of time related output and analyze your model's dynamics using pencil and paper. Not to improve the analysis of Khlebopros et al. but to increase your understanding of your computer model.

Second, it is obvious that Khlebopros' paper and pencil approach probably limits the analyst to two dimensions and certainly three dimensions of the problem at hand. I would think that the methods supplied, while loosing some of their attractive simplicity, are receptive to computerization, bringing them back into the realm of tools we like to use while increasing their applicability.

At the end of this review I long to get rid of the somewhat depressing feeling that crept on me after first reading the title of the book so kindly supplied to me by JASSS' review editor. Being a transition scientist I maintain a far more positive relation with catastrophes. In our opinion societal transitions or attractor changes ('catastrophes') are required to get rid of some of the persistent problems on their way to devastate modern society. In my opinion the methods of Khlebopros et al can not only be put to good use in avoiding catastrophes but also to study and incite the radical changes required to avoid some of the catastrophes our society is approaching head on. I therefore suggest changing the title of the book into "avoiding catastrophes in nature and society".


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