% Define the dynamical system

syms x a b c d lambda s t

f = [a*x(1) - b*x(1)*x(2), -c*x(2) + d*x(1)*x(2) + lambda*x(1)^2 + s*x(1)^3 + t*x(1)^4];

% Set parameter ranges

a_range = linspace(-2, 2, 100);

lambda_range = linspace(-5, 5, 200);

% Compute Hopf-bifurcation points

[bif_points_h, ~] = SetupHopf(funcs,'contpar',[2,4],'corpar',[1],'dir',1,'step',0.01);

[Bifurcations_h,HopfPoints_h,~]=br_contn(funcs,bif_points_h,1500);

% Compute Flip-bifurcation points

[bif_points_f, ~] = SetupPOFold(funcs,'contpar',[2,4],'dir',1,'step',0.01);

[Bifurcations_f,PofoldPoints_f,~]=br_contn(funcs,bif_points_f,1500);

% Compute Neimark-Sacker-bifurcation points

[bif_points_n, ~] = SetupPS(funcs,'contpar',[2,4],'corpar',[1],'dir',1,'step',0.01);

[Bifurcations_n,PsPoints_n,~]=br_contn(funcs,bif_points_n,1500);

% Plot bifurcation diagrams for all three types of bifurcations

figure;

subplot(1,3,1)

plot(a_range, real(HopfPoints_h(2,:)), 'LineWidth', 2)

xlabel('a')

ylabel('\lambda')

title('Bifurcation Diagram for Hopf-Bifurcation')

subplot(1,3,2)

plot(a_range, abs(PofoldPoints_f(2,:)), 'LineWidth', 2)

xlabel('a')

ylabel('|x|')

title('Bifurcation Diagram for Flip-Bifurcation')

subplot(1,3,3)

plot(a_range, real(PsPoints_n(2,:)), 'LineWidth', 2)

xlabel('a')

ylabel('\lambda')

title('Bifurcation Diagram for Neimark-Sacker-Bifurcation')

@ joy Bakshi thanks for your quick response and answer.

My pleasure

@ joy bakshi, can u send me that program in a word file on my email: [email protected]

Dear sir, kindly provide me matlab program in word file.