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Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering

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This textbook is aimed at newcomers to nonlinear dynamics and chaos. The presentation stresses analytical methods, concrete examples, and geometric intuition. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems This textbook is aimed at newcomers to nonlinear dynamics and chaos. The presentation stresses analytical methods, concrete examples, and geometric intuition. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. About the Author: Steven Strogatz is in the Center for Applied Mathematics and the Department of Theoretical and Applied Mathematics at Cornell University. Since receiving his Ph.D. from Harvard university in 1986, Professor Strogatz has been honored with several awards, including the E.M. Baker Award for Excellence, the highest teaching award given by MIT.


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This textbook is aimed at newcomers to nonlinear dynamics and chaos. The presentation stresses analytical methods, concrete examples, and geometric intuition. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems This textbook is aimed at newcomers to nonlinear dynamics and chaos. The presentation stresses analytical methods, concrete examples, and geometric intuition. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. About the Author: Steven Strogatz is in the Center for Applied Mathematics and the Department of Theoretical and Applied Mathematics at Cornell University. Since receiving his Ph.D. from Harvard university in 1986, Professor Strogatz has been honored with several awards, including the E.M. Baker Award for Excellence, the highest teaching award given by MIT.

30 review for Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering

  1. 4 out of 5

    Mark Moon

    I skimmed this book while watching the author's corresponding lecture series on YouTube: https://www.youtube.com/playlist?list.... I skimmed this book while watching the author's corresponding lecture series on YouTube: https://www.youtube.com/playlist?list....

  2. 5 out of 5

    Robert

    I found this to be an excellent introduction to the subject, with clear explanations and extremely good organisation of the material. Examples build on each other in a logical fashion and make the pure mathematics concrete by using genuine scientific applications. The subject itself is fascinating and surprisingly mathematically tractable. The early chapters could be handled by anyone with A-level mathematics. Infrequent references to esoteric subjects like point-set topology are made for the sa I found this to be an excellent introduction to the subject, with clear explanations and extremely good organisation of the material. Examples build on each other in a logical fashion and make the pure mathematics concrete by using genuine scientific applications. The subject itself is fascinating and surprisingly mathematically tractable. The early chapters could be handled by anyone with A-level mathematics. Infrequent references to esoteric subjects like point-set topology are made for the sake of rigour but in fact can be totally ignored without loss of practical understanding of the techniques. Those needing more advanced material in any particular area will find adequate references. Great stuff!

  3. 4 out of 5

    Santiago Ortiz

    I'm just starting the book, but I already know this is a ★★★★★. This book is a window to Nature. The ratio between deepness and accessibility is amazing, thanks to the well written and clear texts and, specially, the smart and beautiful geometric explanations and qualitative solutions. I'm just starting the book, but I already know this is a ★★★★★. This book is a window to Nature. The ratio between deepness and accessibility is amazing, thanks to the well written and clear texts and, specially, the smart and beautiful geometric explanations and qualitative solutions.

  4. 4 out of 5

    Caroline

    This introduction to nonlinear dynamics is easy and entertaining to read. Those are qualities sorely missing from most math books out there. I recommend it to anyone -- undergraduate, graduate, or beyond -- who needs an excellent, beautifully clear introduction to nonlinear dynamics.

  5. 4 out of 5

    Kyle

    Fixed points, their equilibrium, bifurcation parameters, non-dimensionalization, linearization, romeo and juliet

  6. 5 out of 5

    Daniel Brandtner

    Strogatz delivers a readable and comprehensible introduction to nonlinear systems and chaos. He prefers intuitive explanations and examples to rigorous mathematical proofs (though he always indicates where one could find more detailed analysis).

  7. 5 out of 5

    minhhai

    Excellent introductory book on nonlinear dynamics. It's pedagogical, practical and very entertaining, albeit the topics are quite abstract. Strogatz finds effective ways to convey unfamiliar concepts such as limit cycle, bifurcation, strange atractor, Cantor set, to a broad range of educated readers. Many real-world examples in Physics, Biology illustrate the concepts as well as keep readers intrigued. The book is self-contained and requires only some familiarity with one- and multi-variable calc Excellent introductory book on nonlinear dynamics. It's pedagogical, practical and very entertaining, albeit the topics are quite abstract. Strogatz finds effective ways to convey unfamiliar concepts such as limit cycle, bifurcation, strange atractor, Cantor set, to a broad range of educated readers. Many real-world examples in Physics, Biology illustrate the concepts as well as keep readers intrigued. The book is self-contained and requires only some familiarity with one- and multi-variable calculus. Since the topics are abstract in nature, it requires a great deal of visualization, both on the pages and in the reader's head. So it's accessible to anyone who are interested in or working on complex systems in Physics, Biology, Engineering and even Sociology. The most attractive feature of the book is its intuitive and practical approach which focuses entirely on helping readers to develop intuition and basic techniques so that they can apply to their problems, and trims down the pedantic math details. The author softens the solemn development of concepts, usually found in hard-core math books, with insights, anecdotes and humors. The writing is excellent: Many illustrations, carefully chosen examples and instructive structure. This is the most engaging and fun to read that I've known.

  8. 5 out of 5

    Johannes

    This is the book for nonlinear dynamics. Strogatz's writing is not only easy to follow, but is also pleasant, conversational, and at times even a bit whimsical. The book opens with very simple material, and while it eventually touches on some fairly advanced ideas (eg renormalization), it builds up to that point very carefully, so the student should never feel overwhelmed. The examples and problems are drawn from a wide range of fields, so students from disciplines besides math and physics shoul This is the book for nonlinear dynamics. Strogatz's writing is not only easy to follow, but is also pleasant, conversational, and at times even a bit whimsical. The book opens with very simple material, and while it eventually touches on some fairly advanced ideas (eg renormalization), it builds up to that point very carefully, so the student should never feel overwhelmed. The examples and problems are drawn from a wide range of fields, so students from disciplines besides math and physics should see some connection to their own interests. Some people criticize the book's scope, claiming that it is too limited, but specialized topics such as pattern formation and network dynamics are better reserved for a more advanced course. An excellent complement to the book is the set of lecture notes written by Michael Cross and available on his website: Chaos on the Web.

  9. 4 out of 5

    Erickson

    Excellent introductory text on nonlinear dynamics and chaos, with great examples and exercises covering various fields. It is advised though to read certain examples selectively (e.g. if you are not interested in Josephson junction, then skip it since it is somewhat distracting). But otherwise the narration and content are splendid. It is written in not so rigorous and technical sense - thus more advanced supplement is needed for more advanced purposes. It is also highly advisable to complement t Excellent introductory text on nonlinear dynamics and chaos, with great examples and exercises covering various fields. It is advised though to read certain examples selectively (e.g. if you are not interested in Josephson junction, then skip it since it is somewhat distracting). But otherwise the narration and content are splendid. It is written in not so rigorous and technical sense - thus more advanced supplement is needed for more advanced purposes. It is also highly advisable to complement this text with a proper ODE textbook, which covers the methods from linear stability to chaos properly (e.g. ODE text by Boyce). It has some really great intuition and way of seeing things (e.g. formulating phase space of pendulum as cylinder instead of infinitely many fixed point system), so it helps.

  10. 4 out of 5

    Mangoo

    Excellent mathematical introduction to the dynamics of non-linear systems. The text style is rather informal, and very clear, and many of the concepts and results presented are exposed in an intuitive way. Beginning from uni-dimensional systems and reaching to chaos and strange attractors, there's that typical progressive crescendo in complexity which makes the reading worth and sticking. The book also contains a lot of examples taken from several disciplines (physics, chemistry, population dyna Excellent mathematical introduction to the dynamics of non-linear systems. The text style is rather informal, and very clear, and many of the concepts and results presented are exposed in an intuitive way. Beginning from uni-dimensional systems and reaching to chaos and strange attractors, there's that typical progressive crescendo in complexity which makes the reading worth and sticking. The book also contains a lot of examples taken from several disciplines (physics, chemistry, population dynamics, biology, and so on) and many exercises at the end of chapters. Highly recommended.

  11. 5 out of 5

    DJ

    Dang... Promised myself I wouldn't crack this open until classes were over but couldn't resist. Where will the gateway drug to nonlinear dynamics and chaos lead me? Selling sexual favors and stolen TVs for Lyapunov exponents? Dang... Promised myself I wouldn't crack this open until classes were over but couldn't resist. Where will the gateway drug to nonlinear dynamics and chaos lead me? Selling sexual favors and stolen TVs for Lyapunov exponents?

  12. 4 out of 5

    Elio Nakouzi

    Top quality book. Accessible but powerful. Excellent examples to demonstrate the concepts. Even useful as a course textbook.

  13. 5 out of 5

    George

    Background: I'm an aerospace engineering undergraduate who has been exposed to chaos in differential equations, fluid turbulence, and dynamic meteorology. However, my studies never went into the theory of chaos, as this is more of a math topic than an engineering one. I thought it would be beneficial to read this book so I would have a more complete understanding of chaos. Reaction: I was very satisfied with this book. Strogatz isn't like your usual author of a math textbook. He isn't trying to o Background: I'm an aerospace engineering undergraduate who has been exposed to chaos in differential equations, fluid turbulence, and dynamic meteorology. However, my studies never went into the theory of chaos, as this is more of a math topic than an engineering one. I thought it would be beneficial to read this book so I would have a more complete understanding of chaos. Reaction: I was very satisfied with this book. Strogatz isn't like your usual author of a math textbook. He isn't trying to overwhelm you with theory and proof, rather he introduces the basic concepts and moves quickly onto applications. This type of teaching style is great. If you are in any way looking for a technical book on chaos, this is a great choice. Side Note: I also found myself watching some of Strogatz's lectures online while reading the book. For those that are interested, you can find them here: https://www.youtube.com/playlist?list...

  14. 4 out of 5

    Joe

    This is the definitive textbook about nonlinear dynamics, chaos, and complexity sciences. Be forewarned, there’s math - but math is the language of science and everything here is essential and approachable. Not only is this a great introduction, it also makes a solid reference work for later use. Professor Strogatz also has a free companion YouTube series that follows along with the book. Highly recommended.

  15. 5 out of 5

    Ruth

    This is kind of a lie, since we didn't go through the ENTIRE book, but we did cover the first two parts and a bit of the third. I feel like with a better teacher I could have both enjoyed it and learned something from it. I guess we'll never know, now. So long, Strogatz. This is kind of a lie, since we didn't go through the ENTIRE book, but we did cover the first two parts and a bit of the third. I feel like with a better teacher I could have both enjoyed it and learned something from it. I guess we'll never know, now. So long, Strogatz.

  16. 4 out of 5

    Ilknur

    We used this book as a textbook for a differential equations course I took couple years back. Greatly enjoyed the topic and the book. There is a newer edition of this book as of 2015 and I believe the author also has online lectures posted somewhere

  17. 4 out of 5

    tyra

    dense, but not in a good way >_<

  18. 4 out of 5

    Hanah Goetz

    To be honest, this book sparked my love for applied mathematics and is the reason I am currently in a PhD program for biological design.

  19. 5 out of 5

    William

    Excellent introduction to most of the topics mentioned. The chapter on the Lorenz attractor does a great job of giving you the blow-by-blow of the explorative study of a dynamical system.

  20. 5 out of 5

    Robert John Haynie

    Was our textbook for my Nonlinear Dynamics class back in college. Strogatz's language is very clear, at least for junior-senior level math students. Was our textbook for my Nonlinear Dynamics class back in college. Strogatz's language is very clear, at least for junior-senior level math students.

  21. 5 out of 5

    123...N

    Nonlinear Dynamics and Chaos by Strogatz is an introduction to the qualitative study of systems of first degree differential equations. Topics included through the first six chapters (which is as far as I have currently read) are bifurcations, stability of fixed points, linearization about fixed points, and many others. The writing is more conversational than a normal textbook which makes it less painful to read but also has some drawbacks. Cons: The book is harder to use as a reference than typi Nonlinear Dynamics and Chaos by Strogatz is an introduction to the qualitative study of systems of first degree differential equations. Topics included through the first six chapters (which is as far as I have currently read) are bifurcations, stability of fixed points, linearization about fixed points, and many others. The writing is more conversational than a normal textbook which makes it less painful to read but also has some drawbacks. Cons: The book is harder to use as a reference than typical textbooks because definitions and theorems are not boxed and set aside from the rest of the text (though I should note the first time a word is used it is usually in bold text). This can be a problem because the jargon is rather involved. Formal definitions are sometimes not given. Theorems are not accompanied by a proof (though for some of the theorems that is probably a good thing). There is no index of symbols (though to be fair the book has pretty standard notation). The pace is fairly brisk. Pros: A strength of the book is the number of interesting applications provided. Instead of a plain math problem the examples often involve a model of a situation from biology or physics. Overall a very readable math book with interesting examples that stresses developing geometrical intuition and the ability to apply the math above a theoretical and rigorous development of the material. A solid background in calculus is all that is really needed to understand the book, though a having a smattering of linear algebra would be useful at certain points. There is an associated lecture series by the author on youtube. Would Recommend: for people who need a refresher on the subject. People who are familiar with the math but are looking for applications. Would Recommend With Reservations: to people who are new to the subject (the book is well written but the quick pace, difficulty to reference, and lack of rigor can cause problems). Would Not Recommend: for someone looking for a rigorous and theoretical approach to the subject.

  22. 4 out of 5

    Mubarak Alsaeedi

    I studied this book in a course about Dynamical System and Chaos MATH-414 at Kuwait University. We covered the following material: Chapter 1: Overview. In this chapter, the author takes us on a journey about the history of dynamical systems. Chapter 2: One-dimensional flows. It was an intuitive introduction to the subject by showing the qualitative approach to the differential equations. Chapters 3 and 8: Bifurcations. Here we study the state when there is a qualitative change in the dynamic of the I studied this book in a course about Dynamical System and Chaos MATH-414 at Kuwait University. We covered the following material: Chapter 1: Overview. In this chapter, the author takes us on a journey about the history of dynamical systems. Chapter 2: One-dimensional flows. It was an intuitive introduction to the subject by showing the qualitative approach to the differential equations. Chapters 3 and 8: Bifurcations. Here we study the state when there is a qualitative change in the dynamic of the system. Chapter 5: Linear Systems. This chapter studies the qualitative structure of a two-dimensional system. Chapter 6: Phase Plane. In this chapter, we discuss nonlinear systems. Chapter 7: Limit Cycle. It was about the periodic solutions for the differential equations. Chapter 9: Lorenz Equations. We just took a glimpse of the Lorenz equation and some of its properties. Chapter 10: One-dimensional Maps. This chapter deals with a new class of dynamical systems in which time is discrete, rather than continuous. Chapter 11: Fractals. This chapter talks about fractals. Fractals are complex geometric shapes with finite structure at arbitrarily small scales. The chapter begins by reviewing some definitions and results from set theory. I like the writing style of Strogatz. He is a good writer.

  23. 4 out of 5

    Stuart Woolf

    4.5 stars. This is probably the best math book I've ever read. The author's approach, which is highly unusual in math, emphasizes intuition and visualization over abstractions and formulae - a winning strategy because it eases the learning curve for an otherwise difficult subject without stressing the technical details. Some readers will see this as a flaw, but I think the text is balanced correctly: after all, nonlinear dynamics is a field that yields very few analytical solutions, so why waste 4.5 stars. This is probably the best math book I've ever read. The author's approach, which is highly unusual in math, emphasizes intuition and visualization over abstractions and formulae - a winning strategy because it eases the learning curve for an otherwise difficult subject without stressing the technical details. Some readers will see this as a flaw, but I think the text is balanced correctly: after all, nonlinear dynamics is a field that yields very few analytical solutions, so why waste time discussing tools that don't work? The author also does a terrific job making his subject interesting. Some readers might counter that nonlinear dynamics is already interesting to the intended audience, requiring very little reinforcement; this is all true, but in my experience, the average math writer is a curiosity killer. Not so in this text: nonlinear principles are applied somewhat liberally to an array of situations you wouldn't expect, like dating patterns and irreversible insect outbreaks. Another reviewer called the book "a life-changing experience". Admittedly, it is the only book I have read that has made me want to go to graduate school.

  24. 5 out of 5

    Saul

    Very clear and engaging text on nonlinear dynamics with lots of great examples from real-world systems. Rarely do you read a textbook and think to yourself "Wow, I can't wait to find time to work on some of these homework problems." The descriptions often make use of geometric intuition alongside more rigorous derivations, and when the derivations get too difficult, the author omits them in favor of references to more technical works. One little gripe: the figures are sometimes kind of lousy or c Very clear and engaging text on nonlinear dynamics with lots of great examples from real-world systems. Rarely do you read a textbook and think to yourself "Wow, I can't wait to find time to work on some of these homework problems." The descriptions often make use of geometric intuition alongside more rigorous derivations, and when the derivations get too difficult, the author omits them in favor of references to more technical works. One little gripe: the figures are sometimes kind of lousy or copied from much older works from as far back as the '80s and '90s. I could make better figures in a couple hours (and did while working the exercises), so the author could probably have found the time to do so (or had a grad student do it). Some of the problem may be the desire to make everything compatible with two-tone black-and-white for the paper editions. It's a shame, since the fractals are so beautiful when you render them nicely. A second little gripe: The e-book displays equations using little graphic inserts, which are often completely the wrong size. The result is readable enough, but not very attractive.

  25. 5 out of 5

    Michele Cotter

    A really excellent book that served as a fascinating introduction to a complex and pervasive subject. I used the first 8 chapters to get to grips with nonlinear systems for a summer research project and will continue using it for the project and on my own time. Strogatz is a master of communicating complex topics clearly, and emphasizes intuition and understanding the mechanisms at work as the path to understanding the formulae. The book, though written in an almost literary fashion, would probab A really excellent book that served as a fascinating introduction to a complex and pervasive subject. I used the first 8 chapters to get to grips with nonlinear systems for a summer research project and will continue using it for the project and on my own time. Strogatz is a master of communicating complex topics clearly, and emphasizes intuition and understanding the mechanisms at work as the path to understanding the formulae. The book, though written in an almost literary fashion, would probably not be well received by those without a background in calculus and differential equations. As a rising junior in physics, I found it to be a healthy challenge but very accessible. Well worth adding to your shelf.

  26. 5 out of 5

    Milad

    X'(t)=AX+B. That's all we want to solve. This book teaches you how to solve them precisely at some points, but mostly it's all about dynamics and you don't have to be very precise in that area. The examples of the book are also very cool and fun to go through. For example, you analyze how a tumor grows and you even get the power to draw the dynamics in a plot. As another example, you find out about the dynamics of what happens if a specific number of sheep and rabbits are living together in one X'(t)=AX+B. That's all we want to solve. This book teaches you how to solve them precisely at some points, but mostly it's all about dynamics and you don't have to be very precise in that area. The examples of the book are also very cool and fun to go through. For example, you analyze how a tumor grows and you even get the power to draw the dynamics in a plot. As another example, you find out about the dynamics of what happens if a specific number of sheep and rabbits are living together in one place.

  27. 5 out of 5

    Maximiliano Contreras

    Very readable introduction to the basis of Dynamical Systems. A lot of examples and very few mathematical background is required. In that sense is just an introduction; further reading is required to understand deeper concepts (Sharkovsky, for instance). I suggest to watch the lectures in Youtube; makes easier to understand some concepts and have discussions that are not addressed in the book. The references are flawless; contains the angular stones as well as more applied reviewed publications.

  28. 4 out of 5

    Tom

    An excellent overview of the order and structure in chaos. Describes the hisor of the thought in the field, advance, and how it is being applied and may be applied as the field continues to mature. The lecture is very interesting and enthusiatic. I do intend to read some of the materials that he suggested.

  29. 4 out of 5

    Gy

    Dear Professor Strogatz, thanks for brain massacre! :) Great book, fascinating skills of the author to bring closer something that is chaos and nonlinear dynamics. Despite the fact that I've found delight in this book, I'm considering myself as person who lacks the level of knowledge that is "sine qua non" for crafting credible review. Dear Professor Strogatz, thanks for brain massacre! :) Great book, fascinating skills of the author to bring closer something that is chaos and nonlinear dynamics. Despite the fact that I've found delight in this book, I'm considering myself as person who lacks the level of knowledge that is "sine qua non" for crafting credible review.

  30. 4 out of 5

    Kyle

    This book is great. From a perspective of undergraduate math, all the stamp collecting that is obfuscating in defining bifurcations, etc., are presented as clear and simple as possible. There is a minimum of jargon, and just very illustrative examples by worked problems.

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