Timeline for Equilibria Exist in Compact Convex Forward-Invariant Sets
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 24, 2014 at 8:58 | answer | added | user48647 | timeline score: 3 | |
| Aug 11, 2012 at 22:48 | comment | added | Gilles Gnacadja | A colleague showed me an article that essentially has the result: "The Brouwer Fixed Point Theorem Applied to Rumour Transmission", dx.doi.org/10.1016/j.aml.2006.02.007. The article is dated 2005/2006. There have to be earlier references. | |
| Jun 22, 2011 at 1:37 | comment | added | Gilles Gnacadja | Thanks Jaap, for catching and illustrating this insufficiency. I changed the statement. Now I explicitly require the existence of the semiflow. In my intended application, the map $f$ is a polynomial describing the kinetics of a chemical reaction network and time runs from zero to infinity. So I believe it would be too strong to require (global) Lipschitz continuity and too weak to require local Lipschitz continuity. Thanks again. | |
| Jun 22, 2011 at 1:31 | history | edited | Gilles Gnacadja | CC BY-SA 3.0 |
Added the requirement that the dynamical system $\dot{x} = f(x)$ have a semiflow.
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| Jun 21, 2011 at 13:33 | comment | added | Jaap Eldering | Shouldn't you require $f$ to be more than continuous (e.g. Lipschitz)? Currently $f$ doesn't (uniquely) define a (semi-)flow, for example when $f(x) = \sqrt{x}$ in a neighborhood of $x \ge 0$. | |
| Jun 19, 2011 at 0:12 | history | asked | Gilles Gnacadja | CC BY-SA 3.0 |