%% AppendA_Dem
%% Carol Lucas
%% Simulation of 2 equation ODE linear systems:
%% Calls 'odenullcline' which requires 'clode2' for ode45

xinit=[10;-10];I=[10;0];

A1=[-2 -2;1 -6]

%%  One way to find eigenvalues

L1=(trace(A1)-sqrt(trace(A1)^2-4*det(A1)))/2
L2=(trace(A1)+sqrt(trace(A1)^2-4*det(A1)))/2

%%  A second way - actually easiest in Matlab

L=eig(A1)         %  SAME AS:  L=roots([1 -trace(A1) det(A1)])

figure(1);clf;
[t,X1]=odenullcline([0 5],xinit,A1,I);
pause;

figure(1);clf;
[t,X1]=odenullcline([0 5],[20; 0],A1,I);
pause;

figure(1);clf;
[t,X1]=odenullcline([0 5],[20; 10],A1,I);
pause;

figure(1);clf;
[t,X1]=odenullcline([0 5],[-5; 5],A1,I);
pause;

A2=[1 -1;3 6]
figure(2);clf;
[t,X2]=odenullcline([0 .5],xinit,A2,I);
pause;

A3=[-3 5;0 -3]

figure(3);clf;
[t,X3]=odenullcline([0 5],xinit,A3,I);
pause;

A4=[-2 -1;4 1]

figure(4);clf;
[t,X4]=odenullcline([0 20],xinit,A4,I);
pause;

clf;[t,X4]=odenullcline([0 20],[20; 0],A4,I);
pause;

A5=[-1 -1;5 1]

figure(5);clf;
[t,X5]=odenullcline([0 20],xinit,A5,I);
pause;

clf;[t,X5]=odenullcline([0 20],[20; 0],A5,I);
pause;