Timeline for Exponential stability in nonlinear differential equations
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 10, 2013 at 17:46 | vote | accept | Bravo | ||
| Nov 3, 2012 at 14:42 | comment | added | Aaron Hoffman | Define $y(t) = e^{at}x(t)$ so that $\dot{y}(t) = e^{at}f(e^{-at}y) + ay = (f'(0) + a)y + O(y^2)$ with $y \equiv 0$ a solution. If all of the eigenvalues of A have real part less than -a, then by the result you quote $y(t) \to 0$ hence $x(t) \to 0$ at the exponential rate $\sim e^{-at}$. The keywords "exponential weight" and "stable manifold" might be useful. | |
| Nov 3, 2012 at 13:59 | history | edited | Bravo | CC BY-SA 3.0 |
added 274 characters in body
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| Nov 3, 2012 at 12:52 | answer | added | Bazin | timeline score: 2 | |
| Nov 3, 2012 at 1:53 | answer | added | Delio Mugnolo | timeline score: 1 | |
| Nov 3, 2012 at 0:45 | history | asked | Bravo | CC BY-SA 3.0 |