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+clear;

+clc;

+close;

+

+//On linearization we got the following Jacobian "A"

+

+A=[0 -1;1 0];

+t=det(A);

+tau=trace(A);

+

+disp("Since tau = 0 and t>0, thus from chapter 5, (0,0) is a Center")

+disp("And this does not depends on value of a ")

+

+a=-1;

+function xd=linear632(t,x)

+    xd(1)=-x(2)+ a*x(1)*(x(1)^2+x(2)^2);         //x(dot);   x(2) means y.

+    xd(2)=x(1)+a*x(2)*(x(1)^2+x(2)^2);     //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=5;     //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=1:5

+     x0=[x(i);y(i)];

+     t0=0;

+     t=0:0.01:3000;

+     xout=ode(x0,t0,t,linear632);

+     plot2d(xout(1,:),xout(2,:));

+ end

+   xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')

+ figure

+ a=1;

+function xd=linear6322(t,x)

+    xd(1)=-x(2)+ a*x(1)*(x(1)^2+x(2)^2);         //x(dot);   x(2) means y.

+    xd(2)=x(1)+a*x(2)*(x(1)^2+x(2)^2);     //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=35;     //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,linear6322);

+     plot2d(xout(1,:),xout(2,:));

+ end

+   xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')