Without using drawnow command i want plot from below code

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;
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,'.')
    drawnow();
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 getting output as dotted and non fluctuated plot

i want plot like below attachment

please give me the suggestion

Answer 1

[Ishu]

Hi Nune Pratyusha,

I understand that you are trying to plot a 2D graph.

To plot a 2D graph you can use "plot()" function. And the "drawnow()" function is just to see the updates immediately on the screen. It will not have any effect on the resulting graph.

And as you can see you are using "p1 range" for the x-axis and the "p1" are from 1.1 to 1.3, but in the given screenshot x range is from 1-10. And coming to y-axis, in the given screenshot there are 5 "LEs", but you are plotting just the 3 "LEs" and those "LEs" values also does not seem to match with screenshot values.

It is just that the x-axis and y-axis values does not seem to be correct. And to plot all the 5 "LEs" you can plot the "LEs" one after the other and can make use of "hold on" to plot all the "LEs" on the same axes.

For more information onthese function you can refer below MathWorks documentation:

• plot() - https://www.mathworks.com/help/matlab/ref/plot.html?s_tid=doc_ta
• drawnow()- https://www.mathworks.com/help/matlab/ref/drawnow.html?s_tid=doc_ta
• hold on - https://www.mathworks.com/help/matlab/ref/hold.html?searchHighlight=hold%20on&s_tid=srchtitle_support_results_1_hold%20on

Hope it helps.