any thoughts on how to nondimensionlize my set of equations?
- To: mathgroup at smc.vnet.net
- Subject: [mg113312] any thoughts on how to nondimensionlize my set of equations?
- From: dantimatter <google at dantimatter.com>
- Date: Sat, 23 Oct 2010 07:05:39 -0400 (EDT)
... or at the very least, on how to clean them up a bit?
Here are the equations:
p1'[t]==-k6 p1[t]-2*k7 p1[t]^2+2*k8 p1p1[t]+k5 (x1tot-x1p2[t])
p2'[t]==-k10 p2[t]-k1 p2[t] (x1tot-x1p2[t])+k2 x1p2[t]+k9 (x2tot-
p1p1'[t]==k7 p1[t]^2-k8 p1p1[t]-k3 p1p1[t] (x2tot-x2p1p1[t])+k4
x1p2'[t]==k1 p2[t] (x1tot-x1p2[t])-k2 x1p2[t]
x2p1p1'[t]==k3 p1p1[t] (x2tot-x2p1p1[t])-k4 x2p1p1[t]
where p1[t], p2[t], p1p1[t], x1p2[t], x2p1p1[t] are the variables, and
k1, ..., kN and x1tot and x2tot are constants. In the end I want to
find the steady states of the system
(p1'[t]==p2'[t]==p1p1'[t]==x1p2'[t]==x2p1p1'[t]==0), but I'd like to
make the equations as nice and easy to work with as possible, and I'm
not quite sure how to do that. Simply setting the lefthand side to
zero and solving gives me solutions that are pretty messy.
As always, any thoughts that this great community might have would be
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