Book Description
Every form of behavior is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realized how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centered not on the concept of rational players but on the population dynamics of behavioral programs. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions that can alter the basis of their success, i.e., to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions that punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.
Customer Reviews:
The Best There Is On Evolutionary Dynamics.......2000-07-14
When I was writing the chapter on evolutionary dynamics for my book Game Theory Evolving (Princeton, 2000), I looked at all the books available and found nothing. Then Hofbauer and Sigmund's new book (a totally revised version of their earlier Theory of Evolution and Dynamical Systems) came out, and I knew I had a masterpiece in hand.
The book does not assume the reader knows basic differential equation theory--it presents all the theory necessary. Indeed, it is a wonderful way to learn differential equation theory, since one immediately is faced with meaningful problems to solve. It does assume the reader is familiar with multivariate calculus. The book should be accessible to biologists and game theorists with a minimum understanding of each other's disciplines.
There are four parts. First, HS deal with Lotka-Volterra equations of the type prevalent in predator-prey models, which they extend to ecological models and several populations. Like the rest of the book, there are lots of problems and the presentation is elegant and succinct.
The second part deals with game theory dynamics and replicator equations, including sections on evolutionary games and asymmetric games. This too is extremely nicely presented, and the links to the Lotka-Volterra models are made clear.
Part three is on dynamical systems especially of relevance to biochemistry--catalytic hypercycles--as well as higher dimensional phase space dynamics of ecological models.
Part four deal with population genetic models using a differential equation approach. This section is also excellent, though for serious readers it should be complemented by Karlin and Taylor's Second Course in Stochastic Processes (which is much more mathematically demanding).
The physical production of the book is also first rate--a pleasure to read and use.
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Differential Equations and Mathematical Biology
D.S. Jones ,
B.D. Sleeman , and
D. S. Jones
Manufacturer: Chapman & Hall/CRC
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Mathematical Models in Biology (Classics in Applied Mathematics)
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Essential Mathematical Biology
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Mathematical Models in Biology: An Introduction
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Mathematical Biology II
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Computational Cell Biology
ASIN: 1584882964 |
Book Description
The conjoining of mathematics and biology has brought about significant advances in both areas, with mathematics providing a tool for modelling and understanding biological phenomena and biology stimulating developments in the theory of nonlinear differential equations. The continued application of mathematics to biology holds great promise and in fact may be the applied mathematics of the 21st century. Differential Equations and Mathematical Biology provides a detailed treatment of both ordinary and partial differential equations, techniques for their solution, and their use in a variety of biological applications. The presentation includes the fundamental techniques of nonlinear differential equations, bifurcation theory, and the impact of chaos on discrete time biological modelling. The authors provide generous coverage of numerical techniques and address a range of important applications, including heart physiology, nerve pulse transmission, chemical reactions, tumour growth, and epidemics. This book is the ideal vehicle for introducing the challenges of biology to mathematicians and likewise delivering key mathematical tools to biologists. Carefully designed for such multiple purposes, it serves equally well as a professional reference and as a text for coursework in differential equations, in biological modelling, or in differential equation models of biology for life science students.
Book Description
This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. Calcium plays a crucial role in cell physiology, and the study of its dynamics lends insight into many different cellular processes. In particular, calcium plays a central role in muscular contraction, olfactory transduction and synaptic communication, three of the topics to be addressed in detail in this book. In addition to the models, much of the underlying physiology is presented, so that readers may learn both the mathematics and the physiology, and see how the models are applied to specific biological questions.
It is intended primarily as a graduate text or a research reference. It will serve as a concise and up-to-date introduction to all those who wish to learn about the state of calcium dynamics modeling, and how such models are applied to physiological questions.
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Dynamical Systems in Population Biology (CMS Books in Mathematics)
Xiao-Qiang Zhao
Manufacturer: Springer
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ASIN: 0387003088 |
Book Description
The conjoining of nonlinear dynamics and biology has brought about significant advances in both areas, with nonlinear dynamics providing a tool for understanding biological phenomena and biology stimulating developments in the theory of dynamical systems. This research monograph provides an introduction to the theory of nonautonomous semiflows with applications to population dynamics. It develops dynamical system approaches to various evolutionary equations such as difference, ordinary, functional, and partial differential equations, and pays more attention to periodic and almost periodic phenomena. The presentation includes persistence theory, monotone dynamics, periodic and almost periodic semiflows, traveling waves, and global analysis of typical models in population biology. Research mathematicians working with nonlinear dynamics, particularly those interested in applications to biology, will find this book useful. It may also be used as a textbook or as supplementary reading for a graduate special topics course on the theory and applications of dynamical systems. Dr. Xiao-Qiang Zhao is a professor in applied mathematics at Memorial University of Newfoundland, Canada. His main research interests involve applied dynamical systems, nonlinear differential equations, and mathematical biology. He is the author of more than 40 papers and his research has played an important role in the development of the theory of periodic and almost periodic semiflows and their applications.
Book Description
From cell division to heartbeat, clocklike rhythms pervade the activities of every living organism. The cycles of life are ultimately biochemical in mechanism but many of the principles that dominate their orchestration are essentially mathematical.
The Geometry of Biological Time describes periodic processes in living systems and their non-living analogues in the abstract terms of nonlinear dynamics. Enphasis is given in phase singularities, waves, and mutual synchronization in tissues composed of many clocklike units. Also provided are descriptions of the best-studied experimental systems such as chemical oscillators, pacemaker neurons, circadian clocks, and excitable media organized into biochemical and bioelectrical wave patterns in two and three dimensions. No theoretical background is assumed; the required notions are introduced through an extensive collection of pictures and easily understood examples. This extensively updated new edition incorporates the fruits of two decades' further exploration guided by the same principles. Limit cycle theories of circadian clocks are now applied to human jet lag and are understood in terms of the molecular genetics of their recently discovered mechanisms. Supercomputers reveal the unforeseen architecture and dynamics of three-dimensional scroll waves in excitable media. Their role in life-threatening electrical aberrations of the heartbeat is exposed by laboratory experiments and corroborated in the clinic. These developments trace back to three basic mathematical ideas.
Customer Reviews:
A classic.......2007-06-09
This book gets better and better with time. The more I know about the topics covered in this book, the more I realize how important the book is and how much is to be learned from it.
For those not familiar with Art Winfree, he was a pioneer in the mathematical and experimental investigation of the temporal and spatial aspects of biological phenomena. I don't know that I would agree with the reviewer who states that the book "transgresses" scientific boundaries. Perhaps a few decades ago this might have been true, but much of what Winfree pioneered is now mainstream science, or at least well-known.
The idea of "transgressing boundaries" implies a certain sense of rebellion and frequently has polticial overtones, and I would best describe Winfree as an explorer, not a rebel. He, along with a few other scietists scattered throughout various disciplines, followed where his interests and results led him. In a way, this is the essence of pure science.
Later in his life Winfree was recognized in many ways, deservedly so, and continued to work on his ideas until his death. By that time, his work was well known to scientists in a variety of areas. As another reviewer stated, Winfree was not concerned so much with his image, as with explaining his ideas and thought processes that he used in trying to "get it right".
If you are new to the work of Art Winfree this book will serve as a valuable part of your education. If you are an old hand, who has not looked at the material in the book in a long time, it is always worth yet another reading. This is a very good book. It is a classic of science.
Completely Interdisciplinary Science.......2001-08-19
This 2nd edition of a 1980 book is about 50% enlarged. Its readers today will probably be scientists two generations removed from those familiar with the first printing but this review stresses only the new stuff.
The book has two main parts: a first half containing ten chapters mostly about principles and theory, and a second half containing thirteen more about specific experimental systems. It seems curiously hard to decide whether the subject matter is narrow to the point of caricaturing academic specialization, or incredibly broad to the point of suggesting a smorgasbord for science dilettantes. Among the forty thousand academic science journals viable today, not one is devoted to the topic of "biological waves, oscillations, and phase singularities" featured in this book, so it must be too narrow even for such tastes. Yet the literature drawn upon spans an unmatchably wide gamut, ranging from practical medicine to abstract topology, from recent molecular genetics to history of science, from 1836 to 2000. And Science Citations Index shows that the first edition has been cited about a thousand times in widely diverse publications, continuing at about constant rate over the past twenty years. Maybe this is why Springer-Verlag chose to provoke a 2nd edition even after so long.
Updating is usually an opportunity to erase blunders, but this author instead preserves and draws attention to them: how did this mistake happen, and how did the item come to be seen from a different perspective, with different meaning? To avoid giving offense the author preserves mostly his own blunders for such object lessons while going out of his way to credit the innovations of others.
Almost the whole 1980 text is preserved, with new material intercalated on a shaded background, except for two entirely new fat chapters. One concerns the self-organization of excitable media into three-dimensional vortices with exotic topologies. This is almost wholly theoretical (supercomputer calculations and topology): the only ones discovered in the laboratory (so far) are simple vortex rings. The website mentioned in the preface contains much of the same material but more beautifully illustrated in subsequent Powerpoint lectures not mentioned in the book. The other new chapter concerns real cardiology and the role of phase singularities in sudden cardiac death. This seems a morass of details where I would have preferred to see the elegant tree that grew from seeds planted in the first edition. This tree was recognized midway between editions by a medical award normally given only to cardiologists. The new chapter gives the impression that it is already being cut down or at least pruned, and the author is more concerned about the details of that process than about defending its original structure. His 1987 book, was written a few years before the anticipated role of phase singularities and rotors in cardiology found confirmation in quantitative experiments, so the interested reader (if any) must still resort to the cited journal literature for that story.
Another chapter reports on revolutionary developments entirely unforeseen in the first edition: this is the story of molecular genetics of the circadian biological clock. The author provides a readable summary of discoveries up to the end of 1999, but quite a lot of facts have accumulated since that time. The author's point of view is that present-day facts, while unanticipated in detail, do bear out the almost-forgotten theory elaborated in a 1963 book (Goodwin) as to basic principles, and the contrarian expectation stressed in the first edition, that the details may prove to be surprisingly diverse taxonomically.
One of the best resources this eight hundred page book provides is its dual index, with almost two thousand topics and as many cited references, half of them since the first edition. Because the material is both mathematical and experimental, and each item is encountered several times but from different directions in the text, the index is indispensable to persons with finite lifetime who accordingly prefer not to read every word in sequence. Find the topic, jot down its several pages, read one and note a reference from which that argument draws its data, then see the other index for all pages on which that source document is alluded to. The references, by the way, seem exceptionally complete and up-to-date (up to the last day of the 20th century, when it appears the ms was sent to press).
The preface points to a website for Errata. While this may be helpful to specialists, for the rest of us a better discovery lurks nearby: a link to a series of richly illustrated lectures given since the book went to press. These cover much of the same material in about three hundred substantially distinct slides but with entirely different organization in Powerpoint color (in contrast to about as many B&W line drawings in the book). The web site URL changed: it now seems to be eebweb.biosci.Arizona.edu/~art for Errata, and for the Powerpoints, eeb8.biosci.Arizona.edu/art/2000_lectures.
The author was professor of biological sciences at Purdue University until a few years after the first edition, and has since been professor of ecology and evolutionary biology at the University of Arizona. These seem peculiar credentials for authorship of a monograph mostly about topology, physical chemistry, and cardiac electrophysiology in an Applied Mathematics series. The key to understanding this phenomenon may be the first word, standing out in yellow against the green book cover: Interdisciplinary. Whatever may be hyped to the contrary, the academic world resents and resists activities that transgress its historically-defined disciplinary boundaries. You will find them all transgressed in this book.
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The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection (London Mathematical Society Student Texts)
Josef Hofbauer , and
Karl Sigmund
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback
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ASIN: 0521358388 |
Book Description
This textbook is an introduction to dynamical systems and its applications to evolutionary game theory, mathematical ecology, and population genetics. This first English edition is a translation from the authors’ successful German edition which has already made an enormous impact on the teaching and study of mathematical biology. The book’s main theme is to discuss the solution of differential equations that arise from examples in evolutionary biology. Topics covered include the Hardy–Weinberg law, the Lotka–Volterra equations for ecological models, genetic evolution, aspects of sociobiology, and mutation and recombination. There are numerous examples and exercises throughout and the reader is led up to some of the most recent developments in the field. Thus the book will make an ideal introduction to the subject for graduate students in mathematics and biology coming to the subject for the first time. Research workers in evolutionary theory will also find much of interest here in the application of powerful mathematical techniques to the subject.
Book Description
This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.
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Free Energy and Self-Interacting Particles (Progress in Nonlinear Differential Equations and Their Applications)
Takashi Suzuki
Manufacturer: Birkhäuser Boston
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ASIN: 0817643028 |
Book Description
This book examines a nonlinear system of parabolic partial differential equations (PDEs) arising in mathematical biology and statistical mechanics. In the context of biology, the system typically describes the chemotactic feature of cellular slime molds. One way of deriving these equations is via the random motion of a particle in a cellular automaton. In statistical mechanics, on the other hand, the system is associated with the motion of the mean field of self-interacting particles under gravitational force.
Physically, such a system is related to Langevin, Fokker–Planck, Liouville and gradient flow equations, which involve the issues of free energy and the second law of thermodynamics. Mathematically, the mechanism can be referred to as a quantized blowup. Actually, it is regarded as a nonlinear theory of quantum mechanics, and it comes from the mass and location quantization of the singular limit for the associated nonlinear eigenvalue problems. This book describes the whole picture, i.e., the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, the study of equilibrium states via the variational structure derived from the free energy, and the quantized blowup mechanism based on several PDE techniques.
Free Energy and Self-Interacting Particles is suitable for researchers and graduate students of mathematics and applied mathematics who are interested in nonlinear PDEs in stochastic processes, cellular automatons, variational methods, and their applications to natural sciences. It is also suitable for researchers in other fields such as physics, chemistry, biology, and engineering.
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Biological Delay Systems: Linear Stability Theory (Cambridge Studies in Mathematical Biology)
N. MacDonald
Manufacturer: Cambridge University Press
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Binding: Hardcover
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ASIN: 0521340845 |
Book Description
In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for intrinsic delays, due to such things as gestation, maturation or transport. This book is concerned with one of the fundamental questions in the analysis of the effect of delays, namely determining whether they effect the stability of steady states. The analysis is presented for one or two such delays treated both as discrete, where an event which occurred at a precise time in the past has an effect now, and distributed, where the delay is averaged over the population’s history. Both of these types occur in biological contexts. The method used to tackle these questions is linear stability analysis which leads to an understanding of the local stability. By avoiding global questions, the author has kept the mathematical prerequisites to a minimum, essentially advanced calculus and ordinary differential equations.
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