Need help on Phase Diagram

I am new on Matlab. For my undergrad thesis I need to show a phase diagram.

I did this part.

% discrete_model_one_variable

% x(t) = a*x(t-1)
%======================================================
a = 0.92;
b = 0.021;
x = zeros(1,100);

x(1) = 0.36;

for t = 2:100
    x(t) = a*x(t-1)+ b;

end

plot(1:100, x)

But I need a phase diagram. For refernece I am attaching a screenshot what I want.

Can you please guide me how can I get the phase diagram?

Answer 1

[Rahul]

Hi @Atikur,

Assuming you are trying to plot a phase diagram of the given single variable ‘x’ as a discrete function, along with a 45-degree reference line on the same figure, you can plot delayed signal ‘x(t-1)’ ranging from ‘t’ = (1, 99) and the original signal ‘x(t)’ in ‘t’ range of (2, 100).

Here's an updated version of your code that will generate a phase diagram:

% discrete_model_one_variable
% x(t) = a*x(t-1)
%======================================================
a = 0.92;
b = 0.021;
x = zeros(1, 100);
x(1) = 0.36;

% Iterate over time
for t = 2:100
    x(t) = a * x(t-1) + b;
end

% Manually add a point near the origin
% x = [0, x]; % Add an artificial point (x = 0) for visual extrapolation

% Plot phase diagram x(t) vs x(t-1)
figure;
plot(x(1:end-1), x(2:end), 'k-', 'LineWidth', 1.5); % Plot x(t) against x(t-1)
hold on;

% Plot the 45-degree line (x(t) = x(t-1))
plot([0, max(x)], [0, max(x)], 'k--', 'LineWidth', 1); % 45-degree line
xlabel('x(t-1)');
ylabel('x(t)');
legend({'Phase Diagram'; 'Reference 45 deg line'})
title('Phase Diagram of Discrete Model with Extrapolation');
axis equal;
grid on;

• The line plot ’plot(x(1:99), x(2:100), 'k-', 'LineWidth', 1.5)’ plots ‘x(t)’ against ‘x(t-1)’, which creates the phase diagram.
• The line plot ’plot([min(x), max(x)], [min(x), max(x)], 'k--', 'LineWidth', 1)’ adds the 45-degree line (which represents where ‘x(t) = x(t-1)’), from the origin to the max value of 'x(t)'.

I've set the plot to use solid lines ('k-') for the phase diagram and dashed lines ('k--') for the 45-degree line, with appropriate ‘linewidth’ values to make the graph clearer.

For more information regarding functions and parameters mentioned above, refer to the following documentation links:

• Create 2D Line Plots using “plot” function: https://www.mathworks.com/help/simulink/slref/simulink.hmi.instrumentedsignals.html

[Atikur]

Thank you @Rahul for responding!

Could you please guide me on how i can show the directions of this phase diagram?

[Rahul]

Hi @Atikur, I'm unsure of what you are referring to as "directions of the phase diagram", can you describe it further?

[Atikur]

The arrow sign to show on which direction its moving?