Reddit Reddit reviews Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition (Studies in Nonlinearity)

We found 18 Reddit comments about Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition (Studies in Nonlinearity). Here are the top ones, ranked by their Reddit score.

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Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition (Studies in Nonlinearity)
Westview Press
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18 Reddit comments about Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition (Studies in Nonlinearity):

u/mangoismycat · 8 pointsr/math

None of these I've finished, but they're on the backburner whenever I have free time.

A Singular Mathematical Promenade (Etienne Ghys)

Music: A Mathematical Offering (Dave Benson)

Nonlinear Dynamics and Chaos (Strogatz)

u/LargeFood · 7 pointsr/math

Not sure what level you're approaching it from, but Steve Strogatz's Nonlinear Dynamics and Chaos is a pretty good upper-level undergraduate introduction to the topic.

u/LyapunovFunction · 5 pointsr/math

I'm not sure about PDE's, but ODE's are more than just existence and uniqueness theorems. You could argue that the modern study of ODE's is now dynamical systems.

Strogatz's Nonlinear Dynamics and Chaos is a classic if you want to know what applied dynamical systems is like. A more formal text that still captures some interesting ideas is Hale and Kocak's Dynamics and Bifurcations.

Reading textbooks is, of course, a huge time commitment. So perhaps go talk to the dynamical systems people in your department and ask them what is interesting about ODE's. Hell, even go talk to the numerical analysis and do the same for PDE's. Assuming you haven't taken a numerical analysis class, you might be surprised how "pure" numerical analysis feels.

u/snaftyroot · 5 pointsr/dataisbeautiful

once you get into partial differential equations, you'll be able to understand them. the basic ideas are pretty simple. there's just a bunch of computational overhead

this is a great book: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0813349109/ref=dp_ob_title_bk

it's informal and pretty easy to read. I don't remember it being so expensive though. i could've sworn i paid $20 for it

u/ProNate · 4 pointsr/math

Strogatz Nonlinear Dynamics and Chaos covers phase space, phase portraits, and linear stability analysis in great detail with examples from many disciplines including physics. It's probably a good place to start, but I don't think it has very much that's specifically on turbulent fluids. For that, you'll probably want a more focused textbook. Hopefully, someone more knowledgeable can recommend one.

u/jacobolus · 3 pointsr/math

People like “linearizing” problems because it’s a simplification that makes them much easier to solve. It’s like when your Southern African colleague with an unpronounceable name full of clicks gets called “Steve” around the office. That’s not really his name, but eh... if you squint it seems close enough.

If you want to learn about the gnarliness of non-linear problems, Steven Strogatz’s book Nonlinear Dynamics and Chaos is fun and pretty accessible.

u/SofaKingWitty · 3 pointsr/Physics

Strogatz talks about the mathematical details of simpler models of synchronization in his book Nonlinear Dynamics and Chaos. I highly recommend this book: it teaches a wonderful, qualitative way to look at ODEs. The approach is really intuitive, and I wish that I saw it in undergrad. This is also somewhat unrelated, but I know someone who met him, and Strogatz is a super nice guy.

u/mightcommentsometime · 2 pointsr/math

Strogatz is probably the best introductory book on the subject.

When studying nonlinear ODEs, analytical solutions are not always helpful and rarely necessary to understand the behavior of the dynamical system. If you absolutely need an answer (ie for a measured quantity) using RKF 4-5 (adaptive) for anything nonstiff is usually what you would do. There are no real good general tricks besides understanding system behavior without solving the ODE.

If you really want a close approximation, the only other option is to use perturbation theory (multiple scales, WKB, etc) to come up with an approximated solution. But it really isn't worth it in most cases (unless you have some eqution which is singularly perturbed). A good example of this is how to deal with the Schrodinger equation.

As for your example: it is separable, so separate and integrate. But if you have something remotely complicated you either won't get an analytical solution, or it will be such a pain that it isn't useful.

u/frozenbobo · 2 pointsr/Python

For anyone interested in this topic, I can recommend two sources for newcomers.

Conversational, largely non-technical: Chaos: Making a New Science by James Gleick

Technical (requires knowledge of ordinary differential equations, but highly readable): Nonlinear Dynamics and Chaos by Steven H. Strogatz

u/ashen_shugar · 2 pointsr/Physics

In essence what you are interested in is "attractor reconstruction (Takens Theorem)", "measuring the lypaunov exponents", or "finding the correlation dimension". Search around for these things or look them up in a nonlinear dynamics textbook and it should get you on your way.

Check out this paper for a good overview of each of these terms, what they mean, and what they can tell you about your timeseries.
It gives a nice runthrough of the things that you can do with a simple time series to detect any chaos in the signal. They also provide some software which can run their analysis on your own time series.

I also would recommend the book: Nonlinear dynamics and Chaos by Steven Strogatz. Its a fantastic book that lays out a primer for chaotic systems, and its relatively short and not too maths heavy for a textbook.

Finally, this website has some nice pictures of analysis of a number of different chaotic systems that might give a better idea of where you can get started in this area.

u/monghai · 1 pointr/math

This will give you some solid theory on ODEs (less so on PDEs), and a bunch of great methods of solving both ODEs and PDEs. I work a lot with differential equations and this is one of my principal reference books.

This is an amazing book, but it mostly covers ODEs sadly. Both the style and the material covered are great. It might not be exactly what you're looking for, but it's a great read nonetheless.

This covers PDEs from a very basic level. It assumes no previous knowledge of PDEs, explains some of the theory, and then goes into a bunch of elementary methods of solving the equations. It's a small book and a fairly easy read. It also has a lot of examples and exercises.

This is THE book on PDEs. It assumes quite a bit of knowledge about them though, so if you're not feeling too confident, I suggest you start with the previous link. It's something great to have around either way, just for reference.

Hope this helped, and good luck with your postgrad!

u/KnowsAboutMath · 1 pointr/math

> This is an amazing book, but it mostly covers ODEs sadly. Both the style and the material covered are great. It might not be exactly what you're looking for, but it's a great read nonetheless.

This book changed my life. I was all set to become an experimental condensed matter physicist. Then I took a course based on Strogatz... and now I've been a mathematical physicist for the last ten years instead.

u/proteinbased · 1 pointr/chemicalreactiongifs

for anyone interested in chaos, Nonlinear Dynamics and Chaos by Steven Strogatz is a great introduction and among many others topics addresses chaos in chemical reactions.

u/stats_r_us · 1 pointr/math