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clear;
clear;
clc;
close;
set(gca(),"auto_clear","off") //hold on
a=0.4;
b=0.8;
for x=0:0.1:3
y1=a*x;
y2=(x^2)/(b*(1+x^2));
plot2d(x,y1,style=-2)
plot2d(x,y2,style=-3)
end
// Classification of fixed points :
A1=[-a 1;0 -b] //Jacobian at (0,0)
T=trace(A1) //Trace of A
D=det(A1) //Determinant of A
disp("Since, D>0, T<0 , orign is always a fixed point.")
//Now using the arguments given in book and the figure obtained through this example, we conclude :
disp("Middle Fixed Point lies between 0<x*<1, Thus is a Saddle Point.")
disp("The Thied fixed point is with x*>1, Thus always a stable node.")
xtitle("Nullclines--Showing Intersection of x(dot) and y(dot)","x-Axis ( x )","y-Axis ( y )")
figure
a=0.4;
b=0.8;
function xd=linear811(t,x)
xd(1)=-a*x(1)+x(2);
xd(2)=((x(1)^2)/(1+x(1)^2))-b*x(2);
//x(dot); x(2) means y.
//y(dot); x(1) means x.;
endfunction
bound=[0,0,4,4]; //Bounds of x-axis and y-axis as [xmin ymin xmax ymax], change them according to your needs.
nrect=20; //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=1:20
x0=[x(i);y(i)];
t0=0;
t=0:0.01:3000;
xout=ode(x0,t0,t,linear811);
plot2d(xout(1,:),xout(2,:));
end
xtitle('Phase Portrait','x-axis ( x )','y-axis ( y )')
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