Bücher der Reihe Mathematical Modeling

The objective of the workshop was to bring together experts in dynamical systems theory and control theory, and applications workers in both fields, to focus on the problem of controlling nonlinear and potentially chaotic systems using limited control effort.

Designing Innovations in Industrial Logistics Modelling describes practical methods for approaching the task of designing industrial logistics systems.-- Offers models and methods for designing and optimizing industrial logistics systems-- Surveys the development, methodology, and application of logistics models-- Discusses resource optimization and project planning-- Presents successful applications recently employed in advanced industrial companies-- Describes procedures for developing and evaluating new tools and designs

Beginning in 1983, the Swedish Council for Planning and Coordination of Research has organized an annual workshop devoted to some aspect of the behavior and modeling of complex systems. These workshops have been held at the Abisko Research Station of the Swedish Academy of Sciences, a remote location far above the Arctic Circle in northern Sweden. During the period of the midnight sun, from May 4-8, 1987 this exotic venue served as the gathering place for a small group of scientists, scholars, and other connoisseurs of the unknown to ponder the problem of how to model "e;living systems,"e; a term singling out those systems whose principal components are living agents. The 1987 Abisko Workshop focused primarily upon the general system-theoretic concepts of process, function, and form. In particular, a main theme of the Workshop was to examine how these concepts are actually realized in biological, economic, and linguistic situations. As the Workshop unfolded, it became increasingly evident that the central concern of the participants was directed to the matter of how those quintessential aspects of living systems-metabolism, self-repair, and replication-might be brought into contact with the long-established modeling paradigms employed in physics, chemistry, and engineering.

This volume contains the proceedings of the U.S. Australia workshop on Complex Interconnected Biological Systems held in Albany, Western Australia January 1-5, 1989. The workshop was jointly sponsored by the Department of Industry, Trade and Commerce (Australia), and the Na- tional Science Foundation (USA) under the US-Australia agreement. Biological systems are typically hard to study mathematically. This is particularly so in the case of systems with strong interconnections, such as ecosystems or networks of neurons. In the past few years there have been substantial improvements in the mathematical tools available for study- ing complexity. Theoretical advances include substantially improved un- derstanding of the features of nonlinear systems that lead to important behaviour patterns such as chaos. Practical advances include improved modelling techniques, and deeper understanding of complexity indicators such as fractal dimension. Game theory is now playing an increasingly important role in under- standing and describing evolutionary processes in interconnected systems. The strategies of individuals which affect each other's fitness may be incor- porated into models as parameters. Strategies which have the property of evolutionary stabilty result from particular parameter values which may be the main feature of living determined using game theoretic methods. Since systems is that they evolve, it seems appropriate that any model used to describe such systems should have this feature as well. Evolutionary game theory should lead the way in the development of such methods.

Mathematical ecology is the application of mathematics to describe and understand ecosystems. There are two main approaches. One is to describe natural communities and induce statistical patterns or relationships which should generally occur. However, this book is devoted entirely to introducing the student to the second approach: to study deterministic mathematical models and, on the basis of mathematical results on the models, to look for the same patterns or relationships in nature. This book is a compromise between three competing desiderata. It seeks to: maximize the generality of the models; constrain the models to "e;behave"e; realistically, that is, to exhibit stability and other features; and minimize the difficulty of presentations of the models. The ultimate goal of the book is to introduce the reader to the general mathematical tools used in building realistic ecosystem models. Just such a model is presented in Chapter Nine. The book should also serve as a stepping-stone both to advanced mathematical works like Stability of Biological Communities by Yu. M. Svirezhev and D. O. Logofet (Mir, Moscow, 1983) and to advanced modeling texts like Freshwater Ecosystems by M. Straskraba and A. H. Gnauch (Elsevier, Amsterdam, 1985).