Greetings -

I'm having trouble figuring out an efficient means towards solving for the
equilbria in a four-equation model with two herbivores (H1 and H2), and two
predators (P and S).  Below, I have set the rate of change for these
populations to 0 (i.e., equilibrium), then solved.  The resultant solutions
are listed below.  My goal now is to substitute all of these equations back
into "H1", so as to get a general solution for the H1 equilibrium equation
that is dependent only upon parameters....obviously without doing it the
long way.  In sum, I'm looking to develop the equation "H1<-parameters"
from the set of solutions below.  Is this possible with deSolve in R?  I'm
relatively new to this package and despite much reading, can't figure out
any efficient means as of yet.

Advice appreciated,

Peter

H1<-1/alpha11-(alpha12*H2)/alpha11-(apred1*P)/(b1*alpha11)-(ashark1*S)/(b1*alpha11)

H2<-1/alpha22-(alpha21*H1)/alpha22-(apred2*P)/(b2*alpha22)-(ashark2*S)/(b2*alpha22)

S<-(apred1*epred1*H1)/ashark3+(apred2*epred2*H2)/ashark3-xpred/ashark3

P<-(eshark1*ashark1*H1)/(eshark3*ashark3)+(eshark2*ashark2*H2)/(eshark3*ashark3)-xshark/(eshark3*ashark3)


-- 

Peter Houk, PhD
Assistant Professor
University of Guam Marine Laboratory
http://www.guammarinelab.com/peterhouk.html
www.pacmares.com
www.micronesianfishing.com

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