Dynamics Of Complex Interconnected Biological Systems

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.

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.

This book reviews the synergism between various fields of research that are confronted with networks, such as genetic and metabolic networks, social networks, the Internet and ecological systems. In many cases, the interacting networks manifest so-called emergent properties that are not possessed by any of the individual components. Knowledge gained from the study of complex non-biological systems can be applied to the intricate braided relationships that govern cellular functions.

This book is intended as a communication platform to bridge the cultural, conceptual, and technological gap among the key systems biology disciplines of biology, mathematics, and information technology. To support this goal, contributors were asked to adopts an approach that appeals to audiences from different backgrounds.

This is a book book for researchers and practitioners interested in modeling, prediction and forecasting of natural systems based on nonlinear dynamics. It is a practical guide to data analysis and to the development of algorithms, especially for complex systems. Topics such as the characterization of nonlinear correlations in data as dynamical systems, reconstruction of dynamical models from data, nonlinear noise reduction and the limits of predicatability are discussed. The chapters are written by leading experts and consider practical problems such as signal and time series analysis, biomedical data analysis, financial analysis, stochastic modeling, human evolution, and political modeling. The book includes new methods for nonlinear filtering of complex signals, new algorithms for signal classification, and the concept of the "Global Brain".

In recent years experimental and numerical studies have shown that chaos is a widespread phenomenon throughout the biological hierarchy ranging from simple enzyme reactions to ecosystems. Although a coherent picture of the fundamental mechanisms responsible for chaotic dynamics has started to appear it is not yet clear what the implications of such dynamics are for biological systems in general. In some systems it appears that chaotic dynamics are associated with a pathological condi tion. In other systems the pathological condition has regular periodic dynamics whilst the normal non-pathological condition has chaotic dyna mics. Since chaotic behaviour is so ubiquitous in nature and since the phenomenon raises some fundamental questions about its implications for biology it seemed timely to organize an interdisciplinary meeting at which leading scientists could meet to exchange ideas, to evaluate the current state of the field and to stipulate the guidelines along which future research should be directed. The present volume contains the contributions to the NATO Advanced Research Workshop on "Chaos in Biological Systems" held at Dyffryn House, St. Nicholas, Cardiff, U. K. , December 8-12, 1986. At this meeting 38 researchers with highly different backgrounds met to present their latest results through lectures and posters and to discuss the applica tions of non-linear techniques to problems of common interest. . In spite of their involvement in the study of chaotic dynamics for several years many of the participants met here for the first time.