I would really like to see some very simple worked out or with some well pointed hints on these guys. i have two textbooks that outline the idea behind them, but both give only one example that are very contribbed imho. ( Non-Linear dynamics and intro to chaos By Steven H Strogatz) and (differential equations, dynamical systems and intro to chaos by Morris W. Hirsch.) Textbook or links to instructive material on this subject much appreciated. ( im an ungrad and not from math so please don't bludgeon me to death thx.)
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wiki article might be a good start. – TZakrevskiy Jul 20 '13 at 20:15
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Boyce and DiPrima is a popular undergrad diffeq textbook that has a section on this material, with a few examples. – littleO Jul 20 '13 at 20:33
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Note: Be careful that the name is spelled two different ways "Liapunov" or "Lyapunov", so when searching, try both!
These papers might be instructive:
- Lyapunov function methods
- MIT Lectures on Dynamic Systems and Control
- MIT - Finding Lyapunov Functions
- A comparison of three methods of constructing Lyapunov functions
- Stability theory for systems of dierential equations with applications to power control in wireless networks
Books These have a handful of pages each and I like the first two most.
- Modern Control Theory, W. Brogan (very nice write-up on the matter, with physical and electrical circuits)
- The Qualitative Theory of Ordinary Differential Equations, An Introduction, F. Brauer and J.A. Nohel
- Ordinary Differential Equations, V.I. Arnold
- Dynamics and Bifurcations, J. Hale and H Kocak
- Nonlinear systems, H.K. Khalil
There may be some applied materials from Physics areas that might also help.
Amzoti
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