Description
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.
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.
In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting fields as systems biology, evolutionary game theory, and socio-physics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as curiosities of visual perception and the tumultuous love dynamics in Gone with the Wind.
Books arrived quickly in the advertised condition.
My review of the first edition of Nonlinear Dynamics and Chaos follows. Everything I say there applies to the second edition as well. Aside from minor corrections, the second edition differs from the first mainly in the addition of new exercises. Strogatz writes in the Preface
In the twenty years since this book first appeared, the ideas and techniques of nonlinear dynamics and chaos have found application in such exciting new fields as systems biology, evolutionary game theory, and sociophysics. To give you a taste of these recent developments, I’ve added about twenty substantial new exercises that I hope will entice you to learn more.
Review of the First edition
Nonlinear Dynamics is one of the most difficult areas of Applied Mathematics, but you would hardly guess that from reading Steven H. Strogatz. You can read Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering like a (very expensive — but your university library surely has a copy) novel: start at the beginning, and read one page after another until you get to the end. It starts out simple and builds — read in order, it all makes sense — especially if you do the exercises. (Now, be clear: this is a math book. If math is not your thing, you’re not likely to enjoy it.) Few mathematics books, even those about far more tractable subjects, are this readable.
What is “nonlinear dynamics”? “Dynamics” means, roughly, things that change with time. For instance, a car driving from your home to the university library is a dynamic system, and so is a field full of crops that are planted and grow, and so is a disease spreading through a population. This is obviously a big and important subject, and mathematicians have spent much effort on it over the years. They have had most success with linear dynamic systems.
I’m not going to give a technical definition of “linear” — if you’re a mathematician you already know — but in practice it means you can solve a complicated linear problem by breaking it down into simple subproblems whose solutions are known, then combining those simple solutions to produce the solution of the complicated thing. It is the “combining” that linearity makes simple. Linear dynamics is boring (1) because it is mostly a solved problem, and (2) because certain really cool things can never happen in a linear system. For instance, you can have an explosion in a linear system, but there is no way for the explosion to end. If you want to describe a world in which explosions happen, and then stop, and then happen again, you need nonlinearity.
Almost nothing in The Real World™ is truly linear. However, many, many things in The Real World™ are approximately linear. (This is, more or less, what calculus is all about.) Thus linear dynamics allows us to describe all sort of things just up to the point where they get Really Cool And Difficult. Strogatz is here to tell you about the “Really Cool” stuff.
One thing I like about Strogatz’s style is that he works hard to make things clear. There are lots of pictures. Also, he is free of the Pointless Purity fetish that afflicts so many mathematicians. He says, in so many words
Throughout this chapter we have used graphical and analytical methods to analyze first-order systems. Every budding dynamicist should master a third tool: numerical methods.
That is, you are allowed, indeed encouraged, to use a computer! You can never (well seldom) rigorously prove anything with numerical methods, and since proofs are what mathematics is all about, some mathematicians scorn numerical methods. Now, Strogatz is a mathematician. He knows what rigor is and employs it when it’s the best way to an answer. But proofs in nonlinear dynamics are difficult, numerical methods are comparatively easy, and he uses both.
This is the best introduction to Nonlinear Dynamics in existence. If you have any interest in the subject, you should read it. Even if you think you have no interest in the subject, it’s worth a look — you might discover a new love.
The content is good and has improvements over the previous version my only nitpick is the printing quality being much worse in this edition. The paper is quite thin and the printing is a bit blotchy but the plots and everything are still clear. That said the improvements and additions aren’t super huge. While appreicate them they aren’t like mind blowing.
Still I appreciate the high quality of the text and for an undergrad or even a grad student that may not have been exposed to more advanced aspects of ODEs and general non-linearity this remains the best text I know of. I owe it to introducing me to two-timing a technique I still take advantage of to this day.
This is really very good book and written in a proper format. Those who really interested in non linear dynamic theory should read this book
Thank you 🙏
Muy buen libro, bien pedagógico
Está perfecto para iniciar en el mundo de la física y matemática no lineal.
Soy licenciada en física y tengo que recurrir varias veces a este libro para estudiar. 100% recomendado