Timeline for Almost linear ODE: how node becomes a spiral
Current License: CC BY-SA 2.5
5 events
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| Nov 8, 2010 at 18:26 | comment | added | Igor Belegradek | @rpotrie, your example looks like a node in a small neigborhood of the origin. In a larger neigborhood it starts looking like a spiral but my question was about local begavior. Still it is a nice example, thanks! | |
| Nov 8, 2010 at 18:03 | history | edited | Igor Belegradek | CC BY-SA 2.5 |
added 555 characters in body
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| Nov 8, 2010 at 12:39 | comment | added | Igor Belegradek | In a small neighborhood of the equilibrium point $p$, the spiral goes around $p$ infinitely many times, the node does not, so the behaviour is quite different. However, I found an example that does the job. In polar coordinates it looks like $r^\prime=-r$ and $\theta^\prime=1/ln(r)$. | |
| Nov 8, 2010 at 10:03 | comment | added | rpotrie | Maybe I don't understand, but does $x'= -x + y^3$, $y'= -y - x^3$ qualify? However, the spiral and the node are always conjugated, so I don't see quite clearly what you mean by differ (when there are zero eigenvalues this is clear, since you can get, as in your example, really different behaviour). | |
| Nov 8, 2010 at 2:26 | history | asked | Igor Belegradek | CC BY-SA 2.5 |