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Nonlinear Dynamics in Complex Systems: Theory and Applications for the Life-, Neuro- and Natural Sciences, by Armin Fuchs
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With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.
This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work.
“This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.”
“With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.”
“What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.”
(J.A.Scott Kelso, excerpts from the foreword)
- Sales Rank: #2819900 in Books
- Brand: Brand: Springer
- Published on: 2012-09-23
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .63" w x 6.14" l, 1.05 pounds
- Binding: Hardcover
- 238 pages
- Used Book in Good Condition
Review
From the reviews:
“The style of writing is makes the reading interesting. At the same time the author maintains the necessary mathematical rigor. A couple of very appealing features of this book are numerical procedures and computer simulations using the standard software MATLAB and solutions provided at the end of the book to the problems at the end of each chapter. These features make this book an excellent choice for both self-reading and for teaching a course and is a welcome addition to the literature … .” (D. Subbaram Naidu, Amazon.com, November, 2013)
“In a clear and unified approach, elementary notions and concepts of nonlinear dynamical systems are briefly presented, via simple examples, and then implemented in some advanced applications. The book is organized in three parts with each of them containing several chapters. … chapters conclude with problems. … The solutions to all proposed exercises are provided as well, in a corresponding section … . I recommend this book for school and university libraries … .” (Marius-Florin Danca, Mathematical Reviews, April, 2013) From the Back Cover
With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work.“This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.”“With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.”“What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.”(J.A.Scott Kelso, excerpts from the foreword)
Most helpful customer reviews
1 of 1 people found the following review helpful.
An excellent book covering non linear dynamics
By Ron Toolsie
An excellent book covering non linear dynamics. It is well written and more importantly reads well, conveying the points in a brief yet illustrative fashion. It is also quite concise-moreso than Strogatz book, but appears just as comprehesive-apart from being slanted more to those with trajectories toward careers in biomedical research. There is a welcome chapter towards the end on the essential math methods required, which again would be very useful to those without a mathematically intensive background. There are a few minor first-edition bugs in the labeling of some diagram, but this is unlikely to be noticed by all but the most fastidious of readers.
There is an entire chapter dedicated to the HKB model, which is not entirely surprising seeing that Dr K wrote the forward.
If you are interested in NLD, and are torn between which of the two books to get, Fuchs or Strogatz, do what I did-get them both. The Strogatz has more applications and examples outside of the biomedical field and is quite inexpensive. Either I believe will serve you well.
2 of 3 people found the following review helpful.
Nonlinear Dynamics in Complex Systems
By D. Subbaram Naidu
FUCHS, Amin, Nonlinear Dynamics in Complex Systems: Theory and Applications for the Life-, Neuro- and Natural Sciences, ISBN 978-3-642-33552-5, 236 pages, Springer, 2013
Reviewed by D. Subbaram Naidu, Idaho State University (formerly Book Review Editor: IEEE Transactions on Automatic Control; Wiley International Journals of Robust and Nonlinear Control and Optimal Control: Applications and Methods and Elsevier International Journal Mechatronics: The Science of Intelligent Machines).
This book presents a mathematical treatment of various dynamical systems arising in the so-called “soft” life, neuro and natural sciences. The book consists of three parts: Part I covering one-, two- and higher-dimensional systems including chaos and discrete maps and stochastic systems. Part II focusses mainly on Haken-Kelso-Bunz (HKB) Model for human movement behavior and Part III providing mathematical background necessary for the book including some numerical solutions.
The style of writing is makes the reading interesting. At the same time the author maintains the necessary mathematical rigor. A couple of very appealing features of this book are numerical procedures and computer simulations using the standard software MATLAB and solutions provided at the end of the book to the problems at the end of each chapter. These features make this book an excellent choice for both self-reading and for teaching a course and is a welcome addition to the literature [1-3].
References
[1] F.L. Chernoousko and L. Felix and I.M. Ananievski and S.A. Reshmin, Control of Nonlinear Dynamical Systems: Methods and Applications, Springer-Verlag, Berlin, Germany, 2008.
[2] D.Cheng and X. Hu and T. Shen, Analysis and Design of Nonlinear Control Systems, Science Press and Springer-Verlag, Beijing, China and Berlin, Germany, 2010.
[3] K.M. Hangos and J. Boker and G. Szederikenyi, Analysis and Control of Nonlinear Process Systems,
Springer-Verlag, London, UK, 2004.
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