How to define legend (or assign arrows to each plot)?

In the following code, I have three plots for gamma 60, 80 and -80. But as you can see it is not obvious that which plot related to which gamma. Do you guys have ant solution? (one of the solutions is to plot them seperately, but I want them in a same plot).

%Analytical solution of Duffing equation

%% Matlab code to find the frequency response of Single Duffing oscillator

clear all;

clc;

% Given values

gamma_vec = [60 80 -80]; % Nonlinear Parameter; %1; % Nonlinear Parameter

q = 0.02; % Forcing amplitude

beta = 0.05; % linear damping

w0= 1; % Primary resonance

a=linspace(0.01,2.5,1000); % Range of a

%Finding the values of excitation frequency Omega/w0= F and G.

% And corresponding eigen values

for jj=1:length(gamma_vec)

gamma = gamma_vec(jj);

for ii=1:1:length(a)

F(ii)=(1+3*gamma/(8*w0^2)*a(ii)^2+sqrt((q/(2*w0^2*a(ii)))^2-beta^2));

lamF1=sqrt(-(F(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(F(ii)-w0-9*gamma/(8*w0)*a(ii)^2))-(beta*w0);

lamF2=-sqrt(-(F(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(F(ii)-w0-9*gamma/(8*w0)*a(ii)^2))-(beta*w0);

G(ii)=(1+3*gamma/(8*w0^2)*a(ii)^2-sqrt((q/(2*w0^2*a(ii)))^2-beta^2));

lamG1=sqrt(-(G(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(G(ii)-w0-9*gamma/(8*w0)*a(ii)^2))-(beta*w0);

lamG2=-sqrt(-(G(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(G(ii)-w0-9*gamma/(8*w0)*a(ii)^2))-(beta*w0);

if lamF1==conj(lamG1)% % To terminate the loop

break

else

if gamma>0 % For spring hardening effect

plot(G(ii),a(ii),'b.');

hold on

FG=(F(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(F(ii)-w0-9*gamma/(8*w0)*a(ii)^2)+(beta*w0)^2;

if FG<0

plot(F(ii),a(ii),'r.')

else

plot(F(ii),a(ii),'b.')

end

else

plot(F(ii),a(ii),'b.');

hold on

GF=(G(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(G(ii)-w0-9*gamma/(8*w0)*a(ii)^2)+(beta*w0)^2;

if GF<0

plot(G(ii),a(ii),'r.')

else

plot(G(ii),a(ii),'b.')

end

end

end

end

end

xlim([-1,3]); % Range of x-axis

ylim([0,0.3]); %Range of y-axis

xlabel('Normalised frequency (\Omega/\omega_{0})') % Label of x-axis

ylabel('Normalised amplitude (a)') % Label of y-axis

title_str = sprintf('Frequency response of a nonlinear system', gamma);% Create a formatted string with the values of your variables

% Update the title of your figure

title(title_str);

[Dyuman Joshi]

Firstly, format your code properly and use proper indentation.

Secondly, you are plotting each point individually and not a line, and thus it is not possible to make legends as you wish to make. Instead of plotting each point, store the points in an array and plot after the for loop.

Remove LamF2 and LamG2 if there is no use of them in the code, or define them as -LamF1 and -LamG1.

[Mehrdad Nasirshoaibi]

Thanks

Answer 1

[Bjorn Gustavsson]

Use the output from plot. Something like this:

%Analytical solution of Duffing equation
%% Matlab code to find the frequency response of Single Duffing oscillator
clf
% Given values
gamma_vec = [60 80 -80]; % Nonlinear Parameter; %1; % Nonlinear Parameter
q = 0.02; % Forcing amplitude
beta = 0.05; % linear damping
w0=  1; % Primary resonance
a=linspace(0.01,2.5,1000); % Range of a
psz = 18;
%Finding the values of excitation frequency Omega/w0= F and G.
% And corresponding eigen values
for jj = 1:length(gamma_vec)
  clr1 = rgb2hsv(rand(1,3));
  clr1(2) = clr1(2)^.5;
  clr2 = clr1;
  clr2(1) = rem(clr2(1)+0.5,1);
  clr1 = hsv2rgb(clr1);
  clr2 = hsv2rgb(clr2);
  gamma = gamma_vec(jj);
  for ii = 1:1:length(a)
    F(ii) = (1+3*gamma/(8*w0^2)*a(ii)^2+sqrt((q/(2*w0^2*a(ii)))^2-beta^2));
    lamF1 =  sqrt(-(F(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(F(ii)-w0-9*gamma/(8*w0)*a(ii)^2))-(beta*w0);
    lamF2 = -sqrt(-(F(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(F(ii)-w0-9*gamma/(8*w0)*a(ii)^2))-(beta*w0);
    G(ii) =  (1+3*gamma/(8*w0^2)*a(ii)^2-sqrt((q/(2*w0^2*a(ii)))^2-beta^2));
    lamG1 =  sqrt(-(G(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(G(ii)-w0-9*gamma/(8*w0)*a(ii)^2))-(beta*w0);
    lamG2 = -sqrt(-(G(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(G(ii)-w0-9*gamma/(8*w0)*a(ii)^2))-(beta*w0);
    if lamF1==conj(lamG1)% % To terminate the loop
      break
    else
      if gamma > 0 % For spring hardening effect
        phG1(jj) = plot(G(ii),a(ii),'.','markersize',psz,'color',clr1);
        hold on
        FG = (F(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(F(ii)-w0-9*gamma/(8*w0)*a(ii)^2)+(beta*w0)^2;
        if FG < 0
          phF2(jj) = plot(F(ii),a(ii),'.','markersize',psz,'color',clr2);
        else
          phF1(jj) = plot(F(ii),a(ii),'.','markersize',psz,'color',clr1);
        end
      else
        phF1(jj) = plot(F(ii),a(ii),'.','markersize',psz,'color',clr1);
        hold on
        GF = (G(ii)-w0-3*gamma/(8*w0)*a(ii)^2)*(G(ii)-w0-9*gamma/(8*w0)*a(ii)^2)+(beta*w0)^2;
        if GF < 0
          phG2(jj) = plot(G(ii),a(ii),'.','markersize',psz,'color',clr2);
        else
          phG1(jj) = plot(G(ii),a(ii),'.','markersize',psz,'color',clr1);
        end
      end
    end
  end
end
xlim([-1,3]);  % Range of x-axis
ylim([0,0.3]); %Range of y-axis
xlabel('Normalised frequency (\Omega/\omega_{0})') % Label of x-axis
ylabel('Normalised amplitude (a)') % Label of y-axis
title_str = sprintf('Frequency response of a nonlinear system', gamma);% Create a formatted string with the values of your variables
% Update the title of your figure
title(title_str);
legend([phF1,phF2,phG1],'F1-1','F1-2','F1-3','F2-1','F2-2','G1-1','G1-2','G1-3')

You might want to use some more selective set of colours instead of the random ones generated here. And you'll have to adjust the text in the legend too.

HTH

[Mehrdad Nasirshoaibi]

Thanks