Simulation for a 3D system

\begin{align*}

\begin{split}

x^{\prime}=&f_{1} \left (x,y,z \right )=a(y-\phi(x))\\

y^{\prime}=&f_{2} \left (x,y,z \right )=x-y+z \\

z^{\prime}=&f_{3} \left (x,y,z \right )=-b y

\end{split}

\end{align*}

where, $\phi(x)=\frac{1}{16}x-\frac{1}{6}x$.\\

The above system is my system and i want to make a simulation by varying the parameter a and fixitng b to 14 like in this video https://www.youtube.com/watch?v=nQVWD_R--bU . And i have tried the following code but getting errors. How to fix it?

% Define the differential equations

f1 = @(x, y, z, a) a * (y - phi(x));

f2 = @(x, y, z) x - y + z;

f3 = @(x, y, z, b) -b * y;

% Define phi(x)

phi = @(x) (1/16) * x - (1/6) * x;

% Set initial conditions

x0 = 0;

y0 = 0;

z0 = 0;

% Set constant parameter b

b = 14;

% Create a function handle for the ODEs

odefun = @(t, X, a) [f1(X(1), X(2), X(3), a); f2(X(1), X(2), X(3)); f3(X(1), X(2), X(3), b)];

% Time span

tspan = [0 10];

% Create a figure window

f = figure;

% Set initial value of parameter a

a = 0.5;

% Create a slider to control parameter a

b = uicontrol('Parent',f,'Style','slider','Position',[81,54,419,23],...

'value',a, 'min',0, 'max',1);

bgcolor = f.Color;

bl1 = uicontrol('Parent',f,'Style','text','Position',[50,54,23,23],...

'String','0','BackgroundColor',bgcolor);

bl2 = uicontrol('Parent',f,'Style','text','Position',[500,54,23,23],...

'String','1','BackgroundColor',bgcolor);

bl3 = uicontrol('Parent',f,'Style','text','Position',[240,25,100,23],...

'String','Parameter a','BackgroundColor',bgcolor);

% Create a callback function for the slider

b.Callback = @(es,ed) updateSystem(es.Value);

% Function to update the system based on new parameter value of a

function updateSystem(a_value)

% Solve the differential equations

[t, X] = ode45(@(t, X) odefun(t, X, a_value), tspan, [x0; y0; z0]);

% Plot the results

plot(t, X(:, 1), 'r', t, X(:, 2), 'g', t, X(:, 3), 'b');

legend('x', 'y', 'z');

xlabel('Time');

ylabel('Values');

title(['Simulation with a = ', num2str(a_value)]);

end

% Initialize the system with the initial parameter value

updateSystem(a);

I also tried keeping the function in a separate file however still getting errors.

Answer 1

[Abhinav Aravindan]

Hi @Sarowar Hossain,

The issue you are facing is likely due to variable scope in your code. The updateSystem function is unable to access the “Base” workspace variables leading to this error. To resolve this, you may encapsulate your entire code into a function and make relevant modifications to the odefun function handle. Here is a modified code snippet for your reference:

function ODEvisualize
    f = figure('Name', 'ODE Parameter Variation', 'NumberTitle', 'off', ...
               'Position', [100, 100, 600, 400]);

    % Create a slider for parameter 'a'
    uicontrol('Style', 'text', 'Position', [50, 340, 100, 20], 'String', 'Parameter a:');
    a_slider = uicontrol('Style', 'slider', 'Min', 0, 'Max', 10, 'Value', 0.5, ...
                         'Position', [150, 340, 300, 20], ...
                         'Callback', @updatePlot);
    ax = axes('Units', 'pixels', 'Position', [50, 50, 500, 250]);

    % Define the differential equations
    phi = @(x) (1/16) * x - (1/6) * x;
    f1 = @(x, y, z, a) a * (y - phi(x));
    f2 = @(x, y, z) x - y + z;
    f3 = @(x, y, z, b) -b * y;

    % Create a function handle for the ODEs
    odefun = @(t, X, a, b) [f1(X(1), X(2), X(3), a); f2(X(1), X(2), X(3)); f3(X(1), X(2), X(3), b)];

    updatePlot();
    function updatePlot(~, ~)
        % Get the current value of 'a' from the slider
        a = get(a_slider, 'Value');
        b = 14;  % Fixed value of b

        % Solve the ODE
        tspan = [0, 10];
        X0 = [1, 1, 1];  % Initial conditions
        [t, X] = ode45(@(t, X) odefun(t, X, a, b), tspan, X0);

        % Plot the results
        plot(ax, t, X(:, 1), 'r', t, X(:, 2), 'g', t, X(:, 3), 'b');
        xlabel(ax, 'Time');
        ylabel(ax, 'Solution');
        legend(ax, {'x(t)', 'y(t)', 'z(t)'});
        title(ax, sprintf('ODE Solution with a = %.2f', a));
        grid(ax, 'on');
    end
end

Output:

Please find the relevant documentation for your reference.

https://www.mathworks.com/help/matlab/creating_plots/create-callbacks-for-graphics-objects.html

https://www.mathworks.com/help/matlab/ref/ode45.html

https://www.mathworks.com/help/matlab/ref/uicontrol.html

I hope this resolves the errors you are facing!