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.

From the spontaneous rapid firing of cortical neurons to the spatial diffusion of disease epidemics, biological systems exhibit rich dynamic behaviour over a vast range of time and space scales. Unifying many of these diverse phenomena, Dynamics of Biological Systems provides the computational and mathematical platform from which to understand the underlying processes of the phenomena. Through an extensive tour of various biological systems, the text introduces computational methods for simulating spatial diffusion processes in excitable media, such as the human heart, as well as mathematical tools for dealing with systems of nonlinear ordinary and partial differential equations, such as neuronal activation and disease diffusion. The mathematical models and computer simulations offer insight into the dynamics of temporal and spatial biological systems, including cardiac pacemakers, artificial electrical defibrillation, pandemics, pattern formation, flocking behaviour, the interaction of autonomous agents, and hierarchical and structured network topologies. Tools from complex systems and complex networks are also presented for dealing with real phenomenological systems. With exercises and projects in each chapter, this classroom-tested text shows students how to apply a variety of mathematical and computational techniques to model and analyze the temporal and spatial phenomena of biological systems. MATLAB® implementations of algorithms and case studies are available on the author’s website.

Models help us understand the dynamics of real-world processes by using the computer to mimic the actual forces that are known or assumed to result in a system's behavior. This book does not require a substantial background in mathematics or computer science.

This book is intended as a text for a first course on creating and analyzing computer simulation models of biological systems. The expected audience for this book are students wishing to use dynamic models to interpret real data mueh as they would use standard statistical techniques. It is meant to provide both the essential principles as well as the details and equa tions applicable to a few particular systems and subdisciplines. Biological systems, however, encompass a vast, diverse array of topics and problems. This book discusses only a select number of these that I have found to be useful and interesting to biologists just beginning their appreciation of computer simulation. The examples chosen span classical mathematical models of well-studied systems to state-of-the-art topics such as cellular automata and artificial life. I have stressed the relationship between the models and the biology over mathematical analysis in order to give the reader a sense that mathematical models really are useful to biologists. In this light, I have sought examples that address fundamental and, I think, interesting biological questions. Almost all of the models are directly COIIl pared to quantitative data to provide at least a partial demonstration that some biological models can accurately predict.

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 describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.

On three occasions and at different locations, conferences were held to honor the eightieth birthday of Professor Herbert Frohlich: on the 18th December, 1985, in Liverpool, England; on the 14th February, 1986, in Stuttgart, Germany; and on the 8th March, 1986, on the Palm Coast, Florida. This Festschrift is a compilation of the papers of those conferences. Frohlich's choice of problems, from the earliest days, was couched in the phy sics of intrinsically interacting systems of excitation. One example, in which he set the course of research which is still followed, concerned dielectric breakdown, developed from the 1930's over several decades. The interacting systems are the electrons (receiving energy from an electric field) and lattice atom motion (taking energy from the electrons via "electron-phonon" interaction, hence heat dissipa tion). There is a threshold field above which the latter cannot keep up with the former, and the combined system (electrons plus phonons) "runs away"; that is to say, collectively it switches to a new state.

This volume is based on contributions to the second Brain Dynamics Conference, held in Berlin on August 10-14, 1987, as a satellite conference of the Budapest Congress of the International Brain Research Organization. Like the volume resulting from the first conference, Dynamics of Sensory and Cognitive Processing by the Brain, the present work covers new approaches to brain function, with emphasis on electromagnetic fields, EEG, event-related potentials, connectivistic views, and neural networks. Close attention is also paid to research in the emerging field of deterministic chaos and strange attractors. The diversity of this collection of papers reflects a multipronged advance in a hitherto relatively neglected domain, i. e., the study of signs of dynamic processes in organized neural tissue in order both to explain them and to exploit them for clues to system function. The need is greater than ever for new windows. This volume reflects a historical moment, the moment when a relatively neglected field of basic research into available signs of dynamic processes ongoing in organized neural tissue is expanding almost explosively to complement other approaches. From the topics treated, this book should appeal, as did its predecessor, to neuroscientists, neurologists, scientists studying complex systems, artificial intelligence, and neural networks, psychobiologists, and all basic and clinical investigators concerned with new techniques of monitoring and analyzing the brain's electromagnetic activity.

Incorporating chaos theory into psychology and the life sciences, this text includes empirical studies of neural encoding, memory, eye movements, warfare, business cycles and selection of time series analysis algorithms. There are theoretical chapters on emergence and social dynamics, and clinical contributions dealing with: the measurement of quality of life for psychiatric patients; psychosis; the organization of self; and the role of love in family dynamics. Finally ideas from non-linear dynamics are applied to understanding the creative process.

This book presents the fundamental theories, methodologies and case studies of marine ecosystem modeling with a special focus on marine ecological dynamics that could provide scientists and researchers with a stabile and reliabile technical framework to study marine life and their developments.This book also clarifies the research objective and model classification methods of marine ecosystem dynamics research and analyzes the key marine ecological processes that affect modeling. The technical framework for improving the performance of modeling is also proposed, and the latest progress in research, as well as existing difficulties and challenges in end-to-end dynamics models are reviewed and analyzed. A dimensionality reduction theorem is established and derived for analyzing the stability of the solutions of a class of self-conserving marine ecosystem dynamic models. Also included in this work are several new types of marine ecosystem dynamics models constructed by modern computing methods — including artificial neural networks, cellular automata, and statistical dynamics — and case studies.This book is a suitable reference for professional and technical personnel, managers and graduate students specializing in the evolution mechanism, simulation, predication and regulation of marine ecosystems.