Chaos In Biological Systems

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Chaos in Biological Systems

Hans Degn,Arunn V. Holden,Lars Folke Olsen
Chaos in Biological Systems Book PDF

Author : Hans Degn,Arunn V. Holden,Lars Folke Olsen
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 42,9 Mb
Release : 2013-06-29
Category : Science
ISBN : 9781475796315

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Chaos in Biological Systems by Hans Degn,Arunn V. Holden,Lars Folke Olsen Pdf

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.

Chaos in Ecology

J. M. Cushing
Chaos in Ecology Book PDF

Author : J. M. Cushing
Publisher : Elsevier
Page : 248 pages
File Size : 49,8 Mb
Release : 2003
Category : Mathematics
ISBN : 0121988767

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Chaos in Ecology by J. M. Cushing Pdf

Chaos in Ecology is a convincing demonstration of chaos in a biological population. The book synthesizes an ecologically focused interdisciplinary blend of non-linear dynamics theory, statistics, and experimentation yielding results of uncommon clarity and rigor. Topics include fundamental issues that are of general and widespread importance to population biology and ecology. Detailed descriptions are included of the mathematical, statistical, and experimental steps they used to explore nonlinear dynamics in ecology. Beginning with a brief overview of chaos theory and its implications for ecology. The book continues by deriving and rigorously testing a mathematical model that is closely wedded to biological mechanisms of their research organism. Therefrom were generated a variety of predictions that are fundamental to chaos theory and experiments were designed and analyzed to test those predictions. Discussion of patterns in chaos and how they can be investigated using real data follows and book ends with a discussion of the salient lessons learned from this research program Book jacket.

Complex Systems: Chaos and Beyond

Kunihiko Kaneko,Ichiro Tsuda
Complex Systems Chaos and Beyond Book PDF

Author : Kunihiko Kaneko,Ichiro Tsuda
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 47,6 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9783642568619

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Complex Systems: Chaos and Beyond by Kunihiko Kaneko,Ichiro Tsuda Pdf

This book, the first in a series on this subject, is the outcome of many years of efforts to give a new all-encompassing approach to complex systems in nature based on chaos theory. While maintaining a high level of rigor, the authors avoid an overly complicated mathematical apparatus, making the book accessible to a wider interdisciplinary readership.

Nonlinear Dynamics and Chaos

Steven H. Strogatz
Nonlinear Dynamics and Chaos Book PDF

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 55,7 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

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Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Self-Organized Biological Dynamics and Nonlinear Control

Jan Walleczek
Self Organized Biological Dynamics and Nonlinear Control Book PDF

Author : Jan Walleczek
Publisher : Cambridge University Press
Page : 444 pages
File Size : 54,6 Mb
Release : 2006-04-20
Category : Science
ISBN : 9781139427593

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Self-Organized Biological Dynamics and Nonlinear Control by Jan Walleczek Pdf

The growing impact of nonlinear science on biology and medicine is fundamentally changing our view of living organisms and disease processes. This book introduces the application to biomedicine of a broad range of interdisciplinary concepts from nonlinear dynamics, such as self-organization, complexity, coherence, stochastic resonance, fractals and chaos. It comprises 18 chapters written by leading figures in the field and covers experimental and theoretical research, as well as the emerging technological possibilities such as nonlinear control techniques for treating pathological biodynamics, including heart arrhythmias and epilepsy. This book will attract the interest of professionals and students from a wide range of disciplines, including physicists, chemists, biologists, sensory physiologists and medical researchers such as cardiologists, neurologists and biomedical engineers.

Modeling Biological Systems

James W. Haefner
Modeling Biological Systems Book PDF

Author : James W. Haefner
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461541196

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Modeling Biological Systems by James W. Haefner Pdf

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.

Complexity, Analysis and Control of Singular Biological Systems

Qingling Zhang,Chao Liu,Xue Zhang
Complexity Analysis and Control of Singular Biological Systems Book PDF

Author : Qingling Zhang,Chao Liu,Xue Zhang
Publisher : Springer
Page : 236 pages
File Size : 53,7 Mb
Release : 2012-02-16
Category : Technology & Engineering
ISBN : 9781447123033

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Complexity, Analysis and Control of Singular Biological Systems by Qingling Zhang,Chao Liu,Xue Zhang Pdf

Complexity, Analysis and Control of Singular Biological Systems follows the control of real-world biological systems at both ecological and phyisological levels concentrating on the application of now-extensively-investigated singular system theory. Much effort has recently been dedicated to the modelling and analysis of developing bioeconomic systems and the text establishes singular examples of these, showing how proper control can help to maintain sustainable economic development of biological resources. The book begins from the essentials of singular systems theory and bifurcations before tackling the use of various forms of control in singular biological systems using examples including predator-prey relationships and viral vaccination and quarantine control. Researchers and graduate students studying the control of complex biological systems are shown how a variety of methods can be brought to bear and practitioners working with the economics of biological systems and their control will also find the monograph illuminating.

Dynamics of Biological Systems

Michael Small
Dynamics of Biological Systems Book PDF

Author : Michael Small
Publisher : CRC Press
Page : 286 pages
File Size : 52,8 Mb
Release : 2011-08-25
Category : Mathematics
ISBN : 9781439853368

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Dynamics of Biological Systems by Michael Small Pdf

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.

Chaos

Kathleen Alligood,Tim Sauer,J.A. Yorke
Chaos Book PDF

Author : Kathleen Alligood,Tim Sauer,J.A. Yorke
Publisher : Springer
Page : 620 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642592812

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Chaos by Kathleen Alligood,Tim Sauer,J.A. Yorke Pdf

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

Complexity, Chaos, and Biological Evolution

Erik Mosekilde,Lis Mosekilde
Complexity Chaos and Biological Evolution Book PDF

Author : Erik Mosekilde,Lis Mosekilde
Publisher : Springer
Page : 446 pages
File Size : 46,6 Mb
Release : 2012-11-26
Category : Science
ISBN : 1468478494

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Complexity, Chaos, and Biological Evolution by Erik Mosekilde,Lis Mosekilde Pdf

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.

Chaos Control

Guanrong Chen,Xinghuo Yu
Chaos Control Book PDF

Author : Guanrong Chen,Xinghuo Yu
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 45,5 Mb
Release : 2003-07-25
Category : Technology & Engineering
ISBN : 3540404058

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Chaos Control by Guanrong Chen,Xinghuo Yu Pdf

Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. There exists no similar control theory-oriented book available in the market that is devoted to the subject of chaos control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The new technology of chaos control has major impact on novel engineering applications such as telecommunications, power systems, liquid mixing, internet technology, high-performance circuits and devices, biological systems modeling like the brain and the heart, and decision making. The book is not only aimed at active researchers in the field of chaos control involving control and systems engineers, theoretical and experimental physicists, and applied mathematicians, but also at a general audience in related fields.

Chaos and Dynamical Systems

David P. Feldman
Chaos and Dynamical Systems Book PDF

Author : David P. Feldman
Publisher : Princeton University Press
Page : 262 pages
File Size : 45,7 Mb
Release : 2019-08-06
Category : Mathematics
ISBN : 9780691161525

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Chaos and Dynamical Systems by David P. Feldman Pdf

Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.

Chaotic Synchronization

Erik Mosekilde,Yuri Maistrenko,Dmitry Postnov
Chaotic Synchronization Book PDF

Author : Erik Mosekilde,Yuri Maistrenko,Dmitry Postnov
Publisher : World Scientific
Page : 444 pages
File Size : 52,6 Mb
Release : 2002
Category : Science
ISBN : 9810247893

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Chaotic Synchronization by Erik Mosekilde,Yuri Maistrenko,Dmitry Postnov Pdf

A guide to the fascinating new concept of chaotic sychronization.

Genomic Control Process

Isabelle Peter,Eric H. Davidson
Genomic Control Process Book PDF

Author : Isabelle Peter,Eric H. Davidson
Publisher : Academic Press
Page : 460 pages
File Size : 50,9 Mb
Release : 2015-01-21
Category : Science
ISBN : 9780124047464

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Genomic Control Process by Isabelle Peter,Eric H. Davidson Pdf

Genomic Control Process explores the biological phenomena around genomic regulatory systems that control and shape animal development processes, and which determine the nature of evolutionary processes that affect body plan. Unifying and simplifying the descriptions of development and evolution by focusing on the causality in these processes, it provides a comprehensive method of considering genomic control across diverse biological processes. This book is essential for graduate researchers in genomics, systems biology and molecular biology seeking to understand deep biological processes which regulate the structure of animals during development. Covers a vast area of current biological research to produce a genome oriented regulatory bioscience of animal life Places gene regulation, embryonic and postembryonic development, and evolution of the body plan in a unified conceptual framework Provides the conceptual keys to interpret a broad developmental and evolutionary landscape with precise experimental illustrations drawn from contemporary literature Includes a range of material, from developmental phenomenology to quantitative and logic models, from phylogenetics to the molecular biology of gene regulation, from animal models of all kinds to evidence of every relevant type Demonstrates the causal power of system-level understanding of genomic control process Conceptually organizes a constellation of complex and diverse biological phenomena Investigates fundamental developmental control system logic in diverse circumstances and expresses these in conceptual models Explores mechanistic evolutionary processes, illuminating the evolutionary consequences of developmental control systems as they are encoded in the genome

Dynamical Systems

Zeraoulia Elhadj
Dynamical Systems Book PDF

Author : Zeraoulia Elhadj
Publisher : CRC Press
Page : 189 pages
File Size : 49,6 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9780429647420

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Dynamical Systems by Zeraoulia Elhadj Pdf

Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.