(*
 * predprey.mma - predator prey analysis
 *
 * RMM, 8 Jul 06
 *)

<<Jac.m

Fpp[H_, L_] := {
  r H (1 - H/k) - a H L / (c + H),
  b a H L / (c + H) - d L
}

(* Find the equilibrium points and extract non-zero eq pt *)
eqpts = Solve[Fpp[H, L] == {0, 0}, {H, L}];
eqpt3 = Simplify[eqpts[[1]]];	(* pick out nontrivial solution *)

(* Save the nominal paramters (see Examples/figures/predprey_dynamics.m) *)
nompar = {r->1.6, d->0.56, b->0.6, k->125, a->3.2, c->50}

(* Compute the linearization around the equilibrium points *)
A1 = Jac[Fpp[H, L], {H, L}] /. eqpts[[1]] /. nompar;
A2 = Jac[Fpp[H, L], {H, L}] /. eqpts[[2]] /. nompar;
A3 = Jac[Fpp[H, L], {H, L}] /. eqpts[[3]] /. nompar;

B1 = Jac[Fpp[H, L], {r}] /. eqpts[[1]] /. nompar;
B2 = Jac[Fpp[H, L], {r}] /. eqpts[[2]] /. nompar;
B3 = Jac[Fpp[H, L], {r}] /. eqpts[[3]] /. nompar;