Dmitry Postnov

Erik Mosekilde

Yuri Maistrenko

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. Contents: Coupled Nonlinear OscillatorsTransverse Stability of Coupled MapsUnfolding the Riddling BifurcationTime-Continuous SystemsCoupled Pancreatic CellsChaotic Phase SynchronizationPopulation Dynamic SystemsClustering of Globally MapsInteracting NephronsCoherence Resonance Oscillators Readership: Students and researchers interested in applying new concepts of chaotic synchronization and clustering to biological systems. Keywords:Reviews:“The book may be interesting for students and scientists who deal with coupled oscillatory systems and biological applications.”Mathematics Abstracts

Applications to Living Systems

Chaotic Synchronization

Lis Mosekilde

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.

Complexity, Chaos, and Biological Evolution

Zhanybai T Zhusubaliyev

' Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description. This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory. The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems. In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general. Contents:On the Dynamics of Nonlinear SystemsBasic Concepts and MethodsRelay Control SystemsBifurcations and Chaotic Oscillations in Relay SystemsChaotic Oscillations in Pulse-Width Modulated SystemsBorder-Collision Bifurcations on a Two-Dimensional TorusBorder-Collision Bifurcations in a Management System Readership: Graduate students and researchers in nonlinear science and chaos theory; electrical and electronic engineers; experts in control theory and in applied mathematics. Keywords:Chaos;Bifurcations;Border-Collision Bifurcations;Piecewise-Smooth Dynamical Systems;Relay Control Systems;Pulse-Width Modulated Control Systems;Power Converters;Human Decision-Making BehaviorReviews:“This book is an important guide for engineers and all scientists working with non-smooth models.”Mathematical Reviews “The book contains interesting examples of piecewise-smooth dynamical systems and its bifurcation phenomena with direct applications … it will certainly be a useful tool for many scientists and engineers.”Zentralblatt MATH '

Applications to Power Converters, Relay and Pulse-Width Modulated Control Systems, and Human Decision-Making Behavior

Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems

Martin Bertau

Hans V. Westerhoff

This first comprehensive survey to cover all pharmaceutically relevant topics provides a comprehensive introduction to this novel and revolutionary tool, presenting both concepts and application examples of biosimulated cells, organs and organisms. Following an introduction to the role of biosimulation in drug development, the authors go on to discuss the simulation of cells and tissues, as well as simulating drug action and effect. A further section is devoted to simulating networks and populations, and the whole is rounded off by a look at the potential for biosimulation in industrial drug development and for regulatory decisions. Part of the authors are members of the BioSim Network of Excellence that encompasses more than 40 academic institutions, pharmaceutical companies and regulatory authorities dealing with drug development; other contributors come from industry, resulting in a cross-disciplinary expert reference.

Erik Mosekilde

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