i am not getting plot

function run_LE_FO_p1(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q,p_min,p_max,n);
hold on;
ne=3;
ext_fcn=@LE_RF_p1;
t_start=0;h_norm=0.02;t_end=10;
x_start=[0.1 0.1 0.1];h=0.02;q=0.998;

p_max=1.3;
p_min=1.1;
n=800;
p_step=(p_max-p_min)/n
p1=p_min;
while p1<=p_max
    lp=FO_Lyapunov_p1(ne,ext_fcn,0,0.02,10,[0.1 0.1 0.1],0.002,0.998,p1)
    p1=p1+p_step;
    plot(p1,lp)
    
end


function LE=FO_Lyapunov_p1(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q,p1);
% Memory allocation
x=zeros(ne*(ne+1),1); 
x0=x;
c=zeros(ne,1);
gsc=c; zn=c;
n_it = round((t_end-t_start)/h_norm);
% Initial values
x(1:ne)=x_start;
i=1;
while i<=ne
    x((ne+1)*i)=1.0;
    i=i+1;
end
t=t_start;
% Main loop
it=1;
while it<=n_it
    % Solutuion of extended ODE system of FO using FDE12 routine
    [T,Y] = FDE12(q,ext_fcn,t,t+h_norm,x,h,p1); 
    t=t+h_norm;
    Y=transpose(Y);
    x=Y(size(Y,1),:); %solution at t+h_norm
    i=1;
    while i<=ne
        j=1;
        while j<=ne;
            x0(ne*i+j)=x(ne*j+i);
            j=j+1;
        end;
        i=i+1;
    end;
    %       construct new orthonormal basis by gram-schmidt
    zn(1)=0.0;
    j=1;
    while j<=ne
        zn(1)=zn(1)+x0(ne*j+1)^2; 
        j=j+1;
       end;
        zn(1)=sqrt(zn(1));
        j=1;
        while j<=ne
            x0(ne*j+1)=x0(ne*j+1)/zn(1); 
            j=j+1;
        end
        j=2;
        while j<=ne
            k=1;
            while k<=j-1
                gsc(k)=0.0;
                l=1;
                while l<=ne;
                    gsc(k)=gsc(k)+x0(ne*l+j)*x0(ne*l+k);
                    l=l+1;
                end
                k=k+1;
            end
            k=1;
            while k<=ne
                l=1;
                while l<=j-1
                    x0(ne*k+j)=x0(ne*k+j)-gsc(l)*x0(ne*k+l);
                    l=l+1;
                end
                k=k+1;
            end;
            zn(j)=0.0;
            k=1;
            while k<=ne
                zn(j)=zn(j)+x0(ne*k+j)^2;
                k=k+1;
            end
            zn(j)=sqrt(zn(j));
            k=1;
            while k<=ne
                x0(ne*k+j)=x0(ne*k+j)/zn(j);
                k=k+1;
            end
            j=j+1;
        end
%       update running vector magnitudes
        k=1;
        while k<=ne;
            c(k)=c(k)+log(zn(k));
            k=k+1;
        end;
%       normalize exponent        
        k=1;
        while k<=ne
            LE(k)=c(k)/(t-t_start);
            k=k+1;
        end
        i=1;
        while i<=ne
            j=1;
            while j<=ne;
                x(ne*j+i)=x0(ne*i+j);
                j=j+1;
            end
            i=i+1;
        end;
        x=transpose(x);
        it=it+1;
end
function f=LE_RF_p1(t,x,p1)
%p is the parameter
f=zeros(9,1);
X= [x(4) x(7) x(10);
    x(5) x(8) x(11);
    x(6) x(9) x(12)];
%RF equations
f(1)=x(2).*(x(3)-1+x(1).*x(1))+0.1*x(1);
f(2)=x(1).*(3*x(3)+1-x(1).*x(1))+0.1*x(2);
f(3)=-2.*x(3).*(p1+x(1).*x(2));
%Jacobian matrix
J=[2*x(1).*x(2)+0.1, x(1).*x(1)+x(3)-1, x(2);
    -3*x(1).*x(1)+3*x(3)+1,0.1,3*x(1);
    -2*x(2).*x(3),-2*x(1).*x(3),-2*(x(1).*x(2)+p1)];
f(4:12)=J*X; % To be modified if ne>3

I am not getting plot

Answer 1

[Voss]

lp seems to always be a 1-by-3 vector and p1 is a scalar. Therefore

plot(p1,lp)

creates three lines, each with one point. You cannot see a line with one point unless it has a data marker. So add a data marker and you'll see something (and add a drawnow and you'll see it update live):

plot(p1,lp,'.');
drawnow();

[nune pratyusha]

it's not working

[nune pratyusha]

for p1=1.1:0.05:1.3;

while p1<=p_max

lp=FO_Lyapunov_p1(ne,ext_fcn,0,0.02,1,[0.1 0.1 0.1],0.002,1,p1)

p1=p1+p_step;

plot(p1,lp,'.')

drawnow();

end

end

i tried this way also but i didn't get any plot

[Voss]

Maybe create a new figure at the beginning of run_LE_FO_p1:

function run_LE_FO_p1(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q,p_min,p_max,n);
figure();
hold on;

so that the plots don't go into an existing figure that you're not watching.

An m-file containing the code from your question with only those two changes (data marker/drawnow and figure() call) is attached here, and it runs on my machine.

[nune pratyusha]

thanks

[Voss]

welcomes

[nune pratyusha]

sorry to ask again i am implementing above code to 4 dimensional i am getting so many errors please help me

function run_LE_FO_a(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q,a_min,a_max,n);

figure();

hold on;

ne=4;

ext_fcn=@LE_RF_a;

t_start=0;h_norm=0.02;t_end=1;

x_start=[0 0 1 1];h=0.2;q=1;

a_max=-11;

a_min=-12.2;

n=800;

p_step=(a_max-a_min)/n

a=a_min;

% for p1=1.1:0.1:1.3;

while a<=a_max

lp=FO_Lyapunov_a(ne,ext_fcn,0,0.2,1,[0 0 1 1],0.2,1,a)

a=a+p_step;

plot(a,lp,'.')

drawnow();

% end

end

function LE=FO_Lyapunov_a(ne,ext_fcn,t_start,h_norm,t_end,x_start,h,q,a);

% Memory allocation

x=zeros(ne*(ne+1),1);

x0=x;

% y0=x_start

c=zeros(ne,1);

gsc=c; zn=c;

n_it = round((t_end-t_start)/h_norm);

% Initial values

x(1:ne)=x_start;

i=1;

while i<=ne

x((ne+1)*i)=1.0;

i=i+1;

end

t=t_start;

% Main loop

it=1;

while it<=n_it

% Solutuion of extended ODE system of FO using FDE12 routine

[T,Y] = FDE12(q,ext_fcn,t,t+h_norm,[0 0 1 1],h,a);

t=t+h_norm;

Y=transpose(Y);

x=Y(size(Y,1),:); %solution at t+h_norm

i=1;

while i<=ne

j=1;

while j<=ne;

x0(ne*i+j)=x(ne*j+i);

j=j+1;

end;

i=i+1;

end;

% construct new orthonormal basis by gram-schmidt

zn(1)=0.0;

j=1;

while j<=ne

zn(1)=zn(1)+x0(ne*j+1)^2;

j=j+1;

end;

zn(1)=sqrt(zn(1));

j=1;

while j<=ne

x0(ne*j+1)=x0(ne*j+1)/zn(1);

j=j+1;

end

j=2;

while j<=ne

k=1;

while k<=j-1

gsc(k)=0.0;

l=1;

while l<=ne;

gsc(k)=gsc(k)+x0(ne*l+j)*x0(ne*l+k);

l=l+1;

end

k=k+1;

end

k=1;

while k<=ne

l=1;

while l<=j-1

x0(ne*k+j)=x0(ne*k+j)-gsc(l)*x0(ne*k+l);

l=l+1;

end

k=k+1;

end;

zn(j)=0.0;

k=1;

while k<=ne

zn(j)=zn(j)+x0(ne*k+j)^2;

k=k+1;

end

zn(j)=sqrt(zn(j));

k=1;

while k<=ne

x0(ne*k+j)=x0(ne*k+j)/zn(j);

k=k+1;

end

j=j+1;

end

% update running vector magnitudes

k=1;

while k<=ne;

c(k)=c(k)+log(zn(k));

k=k+1;

end;

% normalize exponent

k=1;

while k<=ne

LE(k)=c(k)/(t-t_start);

k=k+1;

end

i=1;

while i<=ne

j=1;

while j<=ne;

x(ne*j+i)=x0(ne*i+j);

j=j+1;

end

i=i+1;

end;

x=transpose(x);

it=it+1;

end

function f=LE_RF_a(t,x,a)

%p is the parameter

f=zeros(16,1);

b=0.4;c=11;d=6;e=130;f1=10;

x=X(1); y=X(2); z=X(3);w=X(4);

Y= [X(5), X(9), X(13), X(17);

X(6), X(10), X(14), X(18);

X(7), X(11), X(15), X(19);

X(8), X(12), X(16), X(20) ];

f(1)=a*y+(0.2+0.2*(abs(w))).*z;

f(2)=b*((w.^2)-13).*z-c*y;

f(3)=-d*x-e*y-f1*z;

f(4)=(z.^2)-w.^2;%Linearized system

Jac=[0 a 0.2+0.2*abs(w) 0.2*w.*z/abs(w);

0 -c b*((w.^2)-13) b*((w*2)-13).*z;

-d -e -f1 0;

0 0 2*z -2*w];

f(5:20)=Jac*Y;

error:>> run_LE_FO_a

p_step =

1.499999999999999e-03

Index exceeds the number of array elements. Index must not exceed 1.

Error in LE_RF_p1 (line 4)

X= [x(4) x(7) x(10);

Error in FDE12>f_vectorfield (line 300)

f = feval(Probl.fdefun,t,y,Probl.param) ;

Error in FDE12 (line 114)

f_temp = f_vectorfield(t0,y0(:,1),Probl) ;

Error in FO_Lyapunov_a (line 21)

[T,Y] = FDE12(q,ext_fcn,t,t+h_norm,[0 0 1 1],h,a);

Error in run_LE_FO_a (line 16)

lp=FO_Lyapunov_a(ne,ext_fcn,0,0.2,1,[0 0 1 1],0.2,1,a)

>>

[Voss]

This question was about getting the plot to show up, which I believe I've answered.

If you have a question about error messages or anything else, please start a new question.

[nune pratyusha]

ok

[nune pratyusha]

with out using drawnow() command i want plot

because graph is comming like dots

i want graph like below attachment