Eigenvalues in symbolic matrix

Hi all,

I'm running the following code to extract eigenvalues from a series of 3x3 symbolic matrices.

The rank of each matrices is 3 so I expect 3 eigenvalues, but I obtain only two eigenvalues.

What I'm doing wrong? Here the code:

Thanks for your help!

Sara

clc

clear all

N0=10/30.97;

vp=[60,50];

kp=[0.5,0.5];

gp=[0.45,0.45];

mp=[1/3/0.001512,1/3/0.001512];%mp=[1/3,1/3];

q=1/100;

rate=2/60;

syms P1 P2 N

[P1eq,P2eq,Neq]=solve([gp(1)*vp(1)./(kp(1)+N0)*N*P1 - mp(1)*P1^2==0, ...

gp(2)*vp(2)./(kp(2)+N0)*N*P2 - mp(2)*P2^2==0, ...

- rate*(N-N0) - q*vp(1)/(kp(1)+N0)*N*P1 - q*vp(2)/(kp(2)+N0)*N*P2==0], [P1,P2,N]);

%% 2.stability analysis

J=jacobian([gp(1)*vp(1)./(kp(1)+N0)*N*P1 - mp(1)*P1^2==0, ...

gp(2)*vp(2)./(kp(2)+N0)*N*P2 - mp(2)*P2^2==0, ...

- rate*(N-N0) - q*vp(1)/(kp(1)+N0)*N*P1 - q*vp(2)/(kp(2)+N0)*N*P2==0], [P1,P2,N]);

%evaluates jacobian in each point

lambda=[];

for i=1:length(P1eq)

M=subs(J,[P1,P2,N],[P1eq(i,1),P2eq(i,1),Neq(i,1)]);

lambda=[lambda;eig(M)'];

end

return;

Answer 1

[Torsten]

Replace

%% 2.stability analysis
J=jacobian([gp(1)*vp(1)./(kp(1)+N0)*N*P1 - mp(1)*P1^2==0, ...
            gp(2)*vp(2)./(kp(2)+N0)*N*P2 - mp(2)*P2^2==0, ...
          - rate*(N-N0) - q*vp(1)/(kp(1)+N0)*N*P1 - q*vp(2)/(kp(2)+N0)*N*P2==0], [P1,P2,N]);

by

%% 2.stability analysis
J=jacobian([gp(1)*vp(1)./(kp(1)+N0)*N*P1 - mp(1)*P1^2, ...
            gp(2)*vp(2)./(kp(2)+N0)*N*P2 - mp(2)*P2^2, ...
            - rate*(N-N0) - q*vp(1)/(kp(1)+N0)*N*P1 - q*vp(2)/(kp(2)+N0)*N*P2], [P1,P2,N])

[sara]

Ops, you're right...

Many thanks!