i need to draw bifurcation and lyapunav for duffing oscillator can anyone help to solve

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chithra A 2014-8-4

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https://ww2.mathworks.cn/matlabcentral/answers/146199-i-need-to-draw-bifurcation-and-lyapunav-for-duffing-oscillator-can-anyone-help-to-solve

function duffing_oscillator clear all

            amp=0.40;             % control parameter 
            alpha=0.5;
            beta=-1.0;
            gamma=1;
            w=1;          
            tspan = 0:0.1:800;    %time step and initial condition
            x10 = 0.5021; x20 = 0.17606;
            y0 = [x10; x20];  
            [~,y] = ode45(@(t,x) f(t,x,alpha,beta,gamma,amp,w),tspan,y0);
            x1=y(:,1); x2=y(:,2);    
            plot(x1,x2);            %plot the variable x and y
            xlabel ('x1');
            ylabel ('x2');
            title('phase portrait of duffing oscillator');
            function dy = f(t,y,alpha,beta,gamma,amp,w)        
            x1 = y(1);    x2 = y(2);  
            dx1=x2;
            dx2=-alpha*x2-beta*x1-gamma*x1^3+amp*sin(w*t);  
            dy = [dx1; dx2];