Erik Mosekilde - Böcker

From time to time, perhaps a few times each century, a revolution occurs that questions some of our basic beliefs and sweeps across otherwise well guarded disciplinary boundaries. These are the periods when science is fun, when new paradigms have to be formulated, and when young scientists can do serious work without first having to acquire all the knowledge of their teachers. The emergence of nonlinear science appears to be one such revolution. In a surprising manner, this new science has disclosed a number of misconceptions in our traditional understanding of determinism. In particular, it has been shown that the notion of predictability, according to which the trajectory of a system can be precisely determined if one knows the equations of motion and the initial conditions, is related to textbook examples of simple; integrable systems. This predictability does not extend to nonlinear, conservative systems in general. Dissipative systems can also show unpredictability, provided that the motion is sustained by externally supplied energy and/or resources. These discoveries, and the associated discovery that even relatively simple nonlinear systems can show extremely complex behavior, have brought about an unprecedented feeling of common interest among scientists from many different disciplines. During the last decade or two we have come to understand that there are universal routes to chaos, we have learned about stretching and folding, and we have discovered the beautiful fractal geometry underlying chaotic attractors.

The development of a proper description of the living world today stands as one of the most significant challenges to physics. A variety of new experimental techniques in molecular biology, microbiol­ ogy, physiology and other fields of biological research constantly expand our knowledge and enable us to make increasingly more detailed functional and structural descriptions. Over the past decades, the amount and complexity of available information have multiplied dramatically, while at the same time our basic understanding of the nature of regulation, behavior, morphogenesis and evolution in the living world has made only modest progress. A key obstacle is clearly the proper handling of the available data. This requires a stronger emphasis on mathematical modeling through which the consistency of the adopted explanations can be checked, and general princi­ ples may be extracted. As an even more serious problem, however, it appears that the proper physical concepts for the development of a theoretically oriented biology have not hitherto been available. Classical mechanics and equilibrium thermody­ namics, for instance, are inappropriate and useless in some of the most essen­ tial biological contexts. Fortunately, there is now convincing evidence that the concepts and methods of the newly developed fields of nonlinear dynam­ ics and complex systems theory, combined with irreversible thermodynamics and far-from-equilibrium statistical mechanics will enable us to move ahead with many of these problems.

Biosimulation is an approach to biomedical research and the treatment of patients in which computer modeling goes hand in hand with experimental and clinical work. Constructed models are used to interpret experimental results and to accumulate information from experiment to experiment.This book explains the concepts used in the modeling of biological phenomena and goes on to present a series of well-documented models of the regulation of various genetic, cellular and physiological processes. The way how the use of computer models allows optimization of cancer treatment for individual patients is discussed and models of interacting nerve cells that can be used to design new treatments for patients with Parkinson's disease are explained. Furthermore this volume provides an overview on the use of models in industry, and presents the view of regulatory agencies on the topic.

Biosimulation is an approach to biomedical research and the treatment of patients in which computer modeling goes hand in hand with experimental and clinical work. Constructed models are used to interpret experimental results and to accumulate information from experiment to experiment.This book explains the concepts used in the modeling of biological phenomena and goes on to present a series of well-documented models of the regulation of various genetic, cellular and physiological processes. The way how the use of computer models allows optimization of cancer treatment for individual patients is discussed and models of interacting nerve cells that can be used to design new treatments for patients with Parkinson's disease are explained. Furthermore this volume provides an overview on the use of models in industry, and presents the view of regulatory agencies on the topic.

Through a series of examples from physics, engineering, biology and economics, this book illustrates the enormous potential for application of ideas and concepts from nonlinear dynamics and chaos theory. The overlap with examples published in other books is virtually equal to zero. The book takes the reader from detailed studies of bifurcation structures of relativity simple models to pattern formation in spatially extended systems. The book also discusses the different perspectives that nonlinear dynamics brings to different fields of science.

Interacting chaotic oscillators are of interest in many areas of physics, biology, and engineering. In the biological sciences, for instance, one of the challenging problems is to understand how a group of cells or functional units, each displaying complicated nonlinear dynamic phenomena, can interact with one another to produce a coherent response on a higher organizational level.This book is a guide to the fascinating new concept of chaotic synchronization. The topics covered range from transverse stability and riddled basins of attraction in a system of two coupled logistic maps over partial synchronization and clustering in systems of many chaotic oscillators, to noise-induced synchronization of coherence resonance oscillators. Other topics treated in the book are on-off intermittency and the role of the absorbing and mixed absorbing areas, periodic orbit threshold theory, the influence of a small parameter mismatch, and different mechanisms for chaotic phase synchronization.The biological examples include synchronization of the bursting behavior of coupled insulin-producing beta cells, chaotic phase synchronization in the pressure and flow regulation of neighboring functional units of the kidney, and homoclinic transitions to phase synchronization in microbiological reactors.

Through a series of examples from physics, engineering, biology and economics, this book illustrates the enormous potential for application of ideas and concepts from nonlinear dynamics and chaos theory. The overlap with examples published in other books is virtually equal to zero. The book takes the reader from detailed studies of bifurcation structures of relativity simple models to pattern formation in spatially extended systems. The book also discusses the different perspectives that nonlinear dynamics brings to different fields of science.