#### asympt() with multiple variables? (16.2.01)

I am trying to simplify several long expressions using the assumption that some constants in the
expression are much larger than others. The expressions are obtained by solving a cubic. Here is the
code

where all \(Kij>0\) and presumably Real (since they represent rate constants). The assumption I want to use to
simplify the expression is K12,K21,K34,K43>>K23,K32).

Is there any way to do this in Maple 6? I have been playing with asympt which works well when I want
to make this kind of assumption for one variable (in a simpler system derived from a cubic), but the
function isn’t deﬁned for multiple variables.

One way would be to write K23= t*k23, K32 = t*k32, and expand in a Taylor series in t. But the
answer is still very messy in this case, even with t=0!

1st answer:

Towards solution:

Is this from chemical kinetics? YES!

chemical reaction

diﬀerential equations

Jacobi matrix

2nd answer:

get Jacobi matrix

switch asymptotics on

switch asymptotics oﬀ

get crude solution (one eigenvalue)

get next (and last) approximation (two values)

Instead of K12,K21,K34,K43 >> K23,K32 I’d like to prefer K23,K32 << K12,K21,K34,K43. Then we
may use mtaylor() as shown in the Maple6 session below.

Unfortunately, I could not ﬁnd another way to force Maple to choose the appropriate branch
cut:

Finally, let us check the solutions: