%-- Aaron Reichow
%-- Mathematical Ecology Matlab log

%-- Log: 4/1/09  Where: Lab --% 
%-- CASE 1: Predation of N1 on N2, No hunting --%

dn1='r*n1*(1-n1/k)-h*n1*n2'
dn2='b*h*n1*n2-m*n2'

%-- CASE 2: Predation of N1 on N2, Hunting on H1 --%

dn1='r*n1*(1-n1/k)-h*n1*n2-h1*n1'
dn2='b*h*n1*n2-m*n2'

%-- CASE 3: Predation of N1 on N2, Hunting on H2 --%

dn1='r*n1*(1-n1/k)-h*n1*n2'
dn2='b*h*n1*n2-m*n2-h2*n2'

%-- CASE 4: Predation of N1 on N2, Hunting on H1, h2 --%

dn1='r*n1*(1-n1/k)-h*n1*n2-h1*n1'
dn2='b*h*n1*n2-m*n2-h2*n2'

%--------------------== Calculations ==--------------------%
%--  --%
[n1hats, n2hats] = solve(dn1,dn2,'n1,n2')

%-- according to jp, these change- don't assume (3,1) is correct --%
n1hat = n1hats(3,1)
n2hat = n2hats(3,1)

w = sym(strcat('[', dn1, ';', dn2, ']'))
v = sym('[n1,n2]')

%-- solve for the jacobian --%
jacob = jacobian(w,v)

%-- solve general expressions for the eigenvalues --%
glambdas = eigensys(jacob)

jac = subs(jacob, n1hat, 'n1')
jac = subs(jac, n2hat, 'n2')

elambdas = eigensys(jac)