Cfrgtkky

so I've given the following problem:

$dn_1/dt=N(t)n_1-n_1$

$dn_2/dt=N(t)n_2-4n_2$

$N(t)=25-6n_1-3n_2$

so I've found the fixed points of the 2 equations and got:
[(0,0),(0,7),(4,0)]

now I want to find the nullclines of them:

so for $dn_1/dt=0$ we get $n_1(24-6n_1-3n_2)$ which means:

1. $n_1=0$ for all $n_2$




2. $n_1=4-0.5n_2$

so for $dn_2/dt=0$ we get $n_2(21-6n_1-3n_2)$ which means:

1. $n_2=0$ for all $n_1$




2. $n_2=7-2n_1$

plotting the following using matlab in order to find the phase plane and basin of attraction gives peculiar results which I can't find to be able to understand. (fig attached below)
I thought the the 3 nullcline need to be intersecting both the fixed points which is more intuitive to me but instead I get the following.

the Matlab code generating this plot is as follows:

clear, close all; clc

%Const

N0=25;

G1=1;G2=1;

a1=6;a2=3;

k1=1;k2=4;

%Params

t0   =   0;      % starting time

dt   =   0.5;    % step size

tEnd = 50;       % end time

timeVec=t0:dt:tEnd;

NumSteps=floor(tEnd./dt);

%Function Handlers

N_t=@(n1,n2) N0-a1.*n1-a2.*n2;

n1_dot=@(n1,n2) G1.*N_t(n1,n2).*n1-k1.*n1;

n2_dot=@(n1,n2) G2.*N_t(n1,n2).*n2-k2.*n2;



%%finding the fixed point's

%%%%%%%%%

system=@(n1,n2) [n1_dot(n1,n2);n2_dot(n1,n2)];

s = solve(system);

%%%%%%%%%



%TODO RECHECK!!!!

%%nulclines

%%%%%%%%%

%n1_dot=0

%case 1: n1  = 0

%case 2: n1 != 0



%n2_dot=0

%case 1: n2  = 0

%case 2: n2 != 0



%%%%%%%%%

ptsMesh=-10:0.2:25;

figure

[X,Y]=meshgrid(ptsMesh);

U=n1_dot(X,Y);

V=n2_dot(X,Y);

normalizedFactor=sqrt(U.^2+V.^2);

quiver(X,Y,U./normalizedFactor,V./normalizedFactor,1,'b')

hold on

plot(s.n1,s.n2,'k*','lineWidth',8)

%plot the trivial nullclines on the axis

[x,y]=size(ptsMesh);

nullclineN1_zero=[0,min(ptsMesh);0,max(ptsMesh)];

nullclineN2_zero=[min(ptsMesh),0;max(ptsMesh),0];

plot(nullclineN2_zero(:,1),nullclineN2_zero(:,2),'g','lineWidth',2);

plot(nullclineN1_zero(:,1),nullclineN1_zero(:,2),'r','lineWidth',2);



t1=@(x2) 4-(0.5).*x2;

res1=t1(ptsMesh);

plot(res1,ptsMesh,'c','lineWidth',2);





t2=@(x1) 7-(2).*x1;

res2=t2(ptsMesh);

plot(ptsMesh,res2,'k','lineWidth',2);

will appreciate some help here
thanks