Yes, it is possible to draw a bifurcation diagram for the rational system ( \frac{1}{1 - ax - bx^2} ) in MATLAB. Here is a step-by-step guide to help you get started:

Here is an example MATLAB code to illustrate this process:

% Define the range for the parameter a a_values = linspace(-2, 2, 1000); % Adjust the range and number of points as needed b = 1; % Set a fixed value for b % Initialize arrays to store results x_values = linspace(-2, 2, 1000); % Adjust the range and number of points as needed y_values = zeros(length(a_values), length(x_values)); % Iterate over the range of a values for i = 1:length(a_values) a = a_values(i); % Define the rational function y = 1 ./ (1 - a * x_values - b * x_values.^2); y_values(i, :) = y; end % Plot the bifurcation diagram figure; imagesc(a_values, x_values, y_values'); colorbar; xlabel('Parameter a'); ylabel('x'); title('Bifurcation Diagram of the System 1/(1 - ax - bx^2)');

This code sets up a range for the parameter (a) and iterates over it, calculating the values of the rational function for each (a). The results are then plotted using imagesc to create a bifurcation diagram.

Thank you Professor.

Welcome

Rajiniganth Pandurangan

Yes, it is possible to draw a bifurcation diagram for the rational system 1/(1-ax-bx^2) in MATLAB. Here's a concise approach: