Plotting different datasets from looped ode45 using subplots.

Hi. I have a script where I'm solving and ode for different values of a parameter. I want to plot each of these cases on a seperate subplot as plotting them all on the same plot is messy. So far i have managed to get the result for the first iteration onto every subplot using:

clc; clear;close all;
% Defining parameters and initial conditions

    f = 0.35+[0.1:0.1:0.4];
    r = 0.3;
    zeta = 0.25;
    eps = -1/6;
    Theta0 = [0.30, 0];
    tspan = [0 100];
    
% Solver options
    opts = odeset('RelTol',1e-6,'AbsTol',[1e-9 1e-9]);
    
% Solver   
   for i = 1:length(f)    
[t,theta] = ode45(@(t,theta) odefcn(t,theta,f(i),r,zeta), tspan,Theta0);
    eqn=@(A) f(i)^2-(-r^2*A+A+(3*eps*A^3)/4)^2-(2*zeta*r*A)^2;
    Amp(:,i)=fzero(eqn,0.1);
    thetaHB=Amp(i).*sin(r.*t);
    theta_HB=Amp(i).*r.*cos(r.*t);

subplot(2,2,1);
plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
pbaspect([1 1 1])
title('f=0.35+0.1');
xlabel ('\theta');
ylabel('d\theta/dt');
legend('Numerical','Harmonic Balance');

subplot(2,2,2);
plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
pbaspect([2 2 1])
title('f=0.35+0.2');
xlabel ('\theta');
ylabel('d\theta/dt');
legend('Numerical','Harmonic Balance');

subplot(2,2,3);
plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
pbaspect([1 1 1])
title('f=0.35+0.3');
xlabel ('\theta');
ylabel('d\theta/dt');
legend('Numerical','Harmonic Balance');

subplot(2,2,4);
plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
pbaspect([1 1 1])
title('f=0.35+0.4');
xlabel ('\theta');
ylabel('d\theta/dt');
legend('Numerical','Harmonic Balance');
sgtitle('Phase Planes r=0.3','FontSize',20)
    end

The underlying function for odefcn is

    function dthetadt = odefcn(t,theta,f,r,zeta)
    dthetadt = zeros(2,1);
    dthetadt(1)=theta(2);
    dthetadt(2)=f.*sin(r.*t)-2.*zeta.*theta(2)-sin(theta(1));
end

Answer 1

[Star Strider]

I assume that the intended result is to have different plots representing the function with different values of ‘f’ in each subplot. The code needs to be tweaked dlightly to get there —

% Defining parameters and initial conditions

f0 = 0.35;
fv = [0.1:0.1:0.4];
r = 0.3;
zeta = 0.25;
eps = -1/6;
Theta0 = [0.30, 0];
tspan = [0 100];

% Solver options
opts = odeset('RelTol',1e-6,'AbsTol',[1e-9 1e-9]);

% Solver   
for i = 1:numel(fv)    
    f = f0 + fv(i);                                                         % Create New 'f' For Each Iteration
    [t,theta] = ode45(@(t,theta) odefcn(t,theta,f,r,zeta), tspan,Theta0);
    eqn=@(A) f^2-(-r^2*A+A+(3*eps*A^3)/4)^2-(2*zeta*r*A)^2;
    Amp(:,i)=fzero(eqn,0.1);
    thetaHB=Amp(i).*sin(r.*t);
    theta_HB=Amp(i).*r.*cos(r.*t);
    
    subplot(3,2,i);                                                         % Iterate Through 'subplot' Array
    plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
    pbaspect([1 1 1])
    title(sprintf('f=0.35+%.1f',fv(i)));
    xlabel ('\theta');
    ylabel('d\theta/dt');
    hl = legend('Numerical','Harmonic Balance');
    hl.Visible = 'off';
    
%     subplot(2,2,2);
%     plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
%     pbaspect([2 2 1])
%     title('f=0.35+0.2');
%     xlabel ('\theta');
%     ylabel('d\theta/dt');
%     legend('Numerical','Harmonic Balance');
%     
%     subplot(2,2,3);
%     plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
%     pbaspect([1 1 1])
%     title('f=0.35+0.3');
%     xlabel ('\theta');
%     ylabel('d\theta/dt');
%     legend('Numerical','Harmonic Balance');
%     
%     subplot(2,2,4);
%     plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
%     pbaspect([1 1 1])
%     title('f=0.35+0.4');
%     xlabel ('\theta');
%     ylabel('d\theta/dt');
%     legend('Numerical','Harmonic Balance');
%     sgtitle('Phase Planes r=0.3','FontSize',20)
end
subplot(3,2,[5 6])
ax = gca;
pos = ax.Position;
hl.Position = pos + [0.1 0.15 -0.2 -0.2];
hl.Visible = 'on';
ax.Visible = 'off';
sgtitle('Phase Planes r=0.3','FontSize',20)

    function dthetadt = odefcn(t,theta,f,r,zeta)
    dthetadt = zeros(2,1);
    dthetadt(1)=theta(2);
    dthetadt(2)=f.*sin(r.*t)-2.*zeta.*theta(2)-sin(theta(1));
end

I re-positioned the legend so that it would not cover the plots, since it was common to all of them.

.

[Frederik Bjerregaard]

Thank you very much!

[Star Strider]

As always, my pleasure!

.