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clear;
clear;
clc;
close;
set(gca(),"auto_clear","off") //hold on
//Get x(dot) = y; y(dot)=x-(x^3);
A1 = [0 1;1 0] //Jacobian at (0,0)
t1=det(A1)
A2 = [0 1;-2 0] //Jacobian at (1,0) and (-1,0).
t2=det(A2)
tau2=trace(A2)
disp("Since, t1=-1, thus (0,0) is a SAddle Point.");
disp("As t2=2 and tau2=0, thus (1,0) and (-1,0) are Centers.");
[x y]=meshgrid(-5:0.5:5,-5:0.5:5);
Nx=21;
Ny=21;
for i=1:21
for j=1:21
E(i,j) = ((1/2)*(y(i,j)^2)) -((1/2)*(x(i,j)^2)) + ((1/4)*(x(i,j)^4));
//contour(x,y,E,3);
end
end
l=-5:0.5:5;
k=-5:0.5:5;
plot3d(l,k,E);
figure
subplot(331)
contour2d(l,k,E,2);
subplot(335)
for x=-2:0.1:2
V=((-1/2)*(x^2))+((1/4)*(x^4));
plot2d(x,V,style=-2)
end
subplot(339)
function xd=linear652(t,x)
xd(1)=x(2);
xd(2)=x(1)-x(1)^3;
//x(dot); x(2) means y.
//y(dot); x(1) means x.;
endfunction
bound=[-4,-4,4,4]; //Bounds of x-axis and y-axis as [xmin ymin xmax ymax], change them according to your needs.
nrect=16; //increase it to get more number of curves, i.e. more information will be available.
set(gca(),"auto_clear","off") //hold on
x=linspace(bound(1),bound(3),nrect);
y=linspace(bound(2),bound(4),nrect);
x0=[];
for i=1:35
x0=[x(i);y(i)];
t0=0;
t=0:0.01:3000;
xout=ode(x0,t0,t,linear652);
plot2d(xout(1,:),xout(2,:));
end
xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')
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