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Universitat de Barcelona, Facultat de Física
The first part introduces and clarifies the main concepts used in the subsequent sections by using particular examples. In a first chapter, Wolker Grimm and Justin M. Calabrese present a primer on resilience, which looks at previous contributions from ecology to engineering. They suggest that resilience is a measure for the ability of a system to return to the reference state after a temporary disturbance. The second chapter, by Sophie Martin, Guillaume Deffuant, and Justin M. Calabrese, lays the foundations for the development of the project's contribution by providing a mathematical definition of resilience. They start from previous definitions, which require that attractors are properly identified in a model and develop a more precise and general definition based on the viability approach. It is important to note that this approach does not need to rely on attractors, even though the latter can be seen as a particular case of the former.
In the second part of the book, the interdisciplinary nature of the team is highlighted as applications in a variety of disciplines are presented. The first case by Xavier Castelló, Federico Vazquez, Victor M. Eguíluz, and Lucía Loureuro-Porto, proposes a model that analyses competition between languages and looks at problems already explored in the social sciences, where any aspects of language viability and language resilience are properly defined. The second application by Dario Taraborelli and Camille Roth, relates to online social systems and illustrates a suitable model of viable Web communities. The third case by Justin M. Calabrese, Guillaume Deffuant, and Wolker Grimm revolves around resilience in Savanna ecosystems. This case is important as it requires models too complex to be computationally analysed in the viability framework and so a prior simplification, capable of keeping the relevant information about the key pattern dynamics, is necessary. Finally, the last case by Nabil Mabrouk, Jean-Denis Mathias, and Guillaume Deffuant presents a bacterial bio-film model, where a simplification of the original detailed model makes the application of viability theory and measures extremely appropriate for this analysis.
Finally, the last part of the book touches upon tools and techniques of the viability approach to resilience. A first contribution by Laetitia Chapel and Guillaume Deffuant helps the reader to understand a particular set of algorithms that approximate viability kernels. Secondly, certain practical examples using KAVIAR (a software developed to use viability kernels) are illustrated that helped to estimate good approximations and controllers. The final chapter by Isabelle Alvarez and Sophie Martin, analyses the robustness of states and trajectories in viability studies.
To sum up, this book is highly recommended to scientists from a wide range of disciplines dealing with complex agent-based systems, where some of the main issues are the calculation of stability of the non-equilibrium states and the robustness under some disturbances. Although ecology has historically been the main candidate to exploit these ideas, it is now clear that they can be implemented in many other fields. Furthermore, this book deals with the limitations of the framework as computational complexity is inherently related to the dimensionality of the problem. Therefore, the lesson is that a good compromise between completeness of the description and reliability of the approach must be reached.
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