Applied Nonlinear Dynamics : A Primer on Stability, Chaos and Fractals

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo­ physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un­ dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.

??Not only are many of the most recent topics included and simply explained, but the reader is also warned against difficulties in the practical implementation of the proposed methods of analysis and against common misinterpretations of some theoretical concepts. Because of its completeness and plain, but mathematically correct, style, this book is also an ideal starting point for researchers from various disciplines who are not familiar with mathematical concepts usually learned in the first two years of university study.?? ??MATHEMATICAL REVIEWS ??I recommend this book strongly both to those who need to teach these topics and to those who want to learn about them, whether or not they are in the biosciences. In fact, I would strongly recommend this book to paleontologists, paleobiologists, paleoecologists, and geologists who are (finally) becoming interested in nonlinear dynamics, but are still afraid to ask.????AMERICAN SCIENTIST ??[The authors] have written a readily accessible introduction to nonlinear dynamics??the book presents the main concepts and applications of nonlinear dynamics at an elementary level??Interspersed in the text are delightful short essays of a page or two each??Courses on nonlinear dynamics rarely present these topics at the level used in the book??It is written in a ??user friendly?? colloquial style and is a delight to read??no reader is likely to encounter a more accessible elementary introduction to nonlinear dynamics.????PHYSICS TODAY

ANot only are many of the most recent topics included and simply explained, but the reader is also warned against difficulties in the practical implementation of the proposed methods of analysis and against common misinterpretations of some theoretical concepts. Because of its completeness and plain, but mathematically correct, style, this book is also an ideal starting point for researchers from various disciplines who are not familiar with mathematical concepts usually learned in the first two years of university study.A AMATHEMATICAL REVIEWS AI recommend this book strongly both to those who need to teach these topics and to those who want to learn about them, whether or not they are in the biosciences. In fact, I would strongly recommend this book to paleontologists, paleobiologists, paleoecologists, and geologists who are (finally) becoming interested in nonlinear dynamics, but are still afraid to ask.AAAMERICAN SCIENTIST A[The authors] have written a readily accessible introduction to nonlinear dynamicsAthe book presents the main concepts and applications of nonlinear dynamics at an elementary levelAInterspersed in the text are delightful short essays of a page or two eachACourses on nonlinear dynamics rarely present these topics at the level used in the bookAIt is written in a Auser friendlyA colloquial style and is a delight to readAno reader is likely to encounter a more accessible elementary introduction to nonlinear dynamics.AAPHYSICS TODAY