It seems like there might be an issue with how the bifurcation parameter b is used in the system dynamics. In the code provided, b is not defined or used in the ODE system. Instead, bifParam is used as the bifurcation parameter in the dydt function.
To fix this issue, you can replace b with bifParam in the dydt function definition, like this:
clear;
% Parameters bifurcationParam = linspace(0, 10, 100); % Range of parameter values for the bifurcation analysis a = rand; % Fixed system parameter a c = rand; % Fixed system parameter c d = rand; % Fixed system parameter d
% Define the ODE system dxdt = @(t, x, y, z) a * (y - x); dydt = @(t, x, y, z, bifParam) x - bifParam * x * z + c * y; dzdt = @(t, x, y, z) x * y + x^2 * z - d * z;
% Bifurcation analysis bifurcationData = zeros(length(bifurcationParam), 100); x0 = [1; 1; 1]; tspan = [0 100];
for i = 1:length(bifurcationParam) currentParam = bifurcationParam(i); odeSystem_i = @(t, X) [ dxdt(t, X(1), X(2), X(3)); dydt(t, X(1), X(2), X(3), currentParam); dzdt(t, X(1), X(2), X(3)); ];
% Compute solution only at specific time points [~, y] = ode113(odeSystem_i, tspan, x0); sampleIndices = round(linspace(1, length(y), 100)); bifurcationData(i, :) = y(sampleIndices, 1)'; end
% Plot bifurcation diagram figure; plot(bifurcationParam, bifurcationData, 'r.', 'MarkerSize', 10); xlabel('Parameter b'); ylabel('x'); title('Bifurcation Diagram');