Comments for Hydrobates
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A mathematician thinks aloudThu, 03 Apr 2014 07:23:34 +0000hourly1http://wordpress.com/Comment on Geometric singular perturbation theory by Proofs of dynamical properties of the MAPK cascade | Hydrobates
http://alanrendall.wordpress.com/2013/11/29/geometric-singular-perturbation-theory/#comment-2180
Thu, 03 Apr 2014 07:23:34 +0000http://alanrendall.wordpress.com/?p=1661#comment-2180[…] description of the same biological system we then used geometric singular perturbation theory (cf. this post) to conclude that the MM-MA system also shows […]
]]>Comment on The multiple futile cycle by Proofs of dynamical properties of the MAPK cascade | Hydrobates
http://alanrendall.wordpress.com/2012/08/27/the-multiple-futile-cycle/#comment-2179
Thu, 03 Apr 2014 07:23:33 +0000http://alanrendall.wordpress.com/?p=1537#comment-2179[…] the dual futile cycle, which can be thought of as the second layer of the cascade in isolation (cf. this post). We proved that the MM system for the dual futile cycle exhibits a generic cusp bifurcation and […]
]]>Comment on Michaelis-Menten theory by Proofs of dynamical properties of the MAPK cascade | Hydrobates
http://alanrendall.wordpress.com/2008/11/15/michaelis-menten-theory/#comment-2178
Thu, 03 Apr 2014 07:23:31 +0000http://alanrendall.wordpress.com/?p=177#comment-2178[…] a quasistationary approximation the result will be called the MM system (for Michaelis-Menten) (cf. this post). With a suitable formulation the MM system is a singular limit of the MM-MA system. The MAPK […]
]]>Comment on Dynamics of the MAP kinase cascade by Proofs of dynamical properties of the MAPK cascade | Hydrobates
http://alanrendall.wordpress.com/2012/04/07/dynamics-of-the-map-kinase-cascade/#comment-2177
Thu, 03 Apr 2014 07:23:28 +0000http://alanrendall.wordpress.com/?p=1356#comment-2177[…] MAP kinase cascade, which I mentioned in a previous post, is a biochemical network which has been subject to a lot of theoretical and experimental study. […]
]]>Comment on Dynamics of the MAP kinase cascade by The Hopf-Hopf bifurcation and chaos in ecological systems | Hydrobates
http://alanrendall.wordpress.com/2012/04/07/dynamics-of-the-map-kinase-cascade/#comment-2004
Tue, 11 Feb 2014 20:04:30 +0000http://alanrendall.wordpress.com/?p=1356#comment-2004[…] point chaos rears its ugly head. The third thing is the fact that it has been suggested that the MAPK cascade, a dynamical system I am very interested in from the point of view of my own research, may exhibit […]
]]>Comment on Interval arithmetic by Rod Carvalho
http://alanrendall.wordpress.com/2014/01/28/interval-arithmetic/#comment-1980
Tue, 28 Jan 2014 20:44:19 +0000http://alanrendall.wordpress.com/?p=1705#comment-1980Brian Hayes wrote a short survey-like paper on interval arithmetic over a decade ago:

The paper is very basic and written for a layperson. The references at the end may interest you, however.

]]>Comment on The practical use of proofs by Interval arithmetic | Hydrobates
http://alanrendall.wordpress.com/2013/07/31/the-practical-use-of-proofs/#comment-1979
Tue, 28 Jan 2014 13:42:36 +0000http://alanrendall.wordpress.com/?p=1642#comment-1979[…] a recent post I wrote about the relations between mathematics and simulations. In doing so I forgot about one […]
]]>Comment on The multiple futile cycle by Monotone dynamical systems | Hydrobates
http://alanrendall.wordpress.com/2012/08/27/the-multiple-futile-cycle/#comment-1978
Sun, 29 Dec 2013 10:00:22 +0000http://alanrendall.wordpress.com/?p=1537#comment-1978[…] systems from systems of chemical reactions by a change of variables has been discussed in a previous post. The advantage of this is that together with other conditions it can be use to show that generic […]
]]>Comment on Albert Goldbeter and glycolytic oscillations by Geometric singular perturbation theory | Hydrobates
http://alanrendall.wordpress.com/2012/01/21/albert-goldbeter-and-glycolytic-oscillations/#comment-1975
Fri, 29 Nov 2013 14:41:54 +0000http://alanrendall.wordpress.com/?p=1292#comment-1975[…] and Lefever (Biophys J. 12, 1302) for glycolysis. It is different from the model I mentioned in a previous post but is also an important part of the chapter of Goldbeter’s book which I discussed there. The […]
]]>Comment on The fold bifurcation by Higher dimensional bifurcations | Hydrobates
http://alanrendall.wordpress.com/2010/02/24/the-fold-bifurcation/#comment-1963
Mon, 09 Sep 2013 08:20:11 +0000http://alanrendall.wordpress.com/?p=890#comment-1963[…] stationary solution for . The case where , and is the fold bifurcation, which was discussed in a previous post. In this case these conditions together with the condition imply topological equivalence to a […]
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