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.

The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.

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".