How to create a function to get bifurcation plot

Question

Gibson.G 2017-4-14

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https://ww2.mathworks.cn/matlabcentral/answers/335311-how-to-create-a-function-to-get-bifurcation-plot

回答： Yulia Verbitskaya 2019-4-23

Study period-doubling in the Lorenz model by examining the behavior for r≤ 160. Claculate the bifurcation diagram and extract the value of Feigenbaum's δ parameter. Hint:While this problem can be done using the Euler method, it is probably advisable, in order to conserve computer time, to use the Runge-Kutta algorithm. Your matlab function should produce one clearly labeled bifurcation line-plot for period doubling->chaos transition in z,as r changes from 25->160.

Hi guys, I'm a totally new one to learn how to use matlab and met this problem. My personal thoughts about this question is firstly create:function [x, y, z, t] = problem(x0y0z0, tmax, dt, r) And my inputs should be x0y0z0 a 1x3 vector containing the initial values for x0, y0 and z0

tmax: the max time to iterate

dt: the step size

r: the range of r values to examine (I want to try the range of 100-160)

and my outputs can be Outputs: x, y, z as functions of time t, all vectors of length ~tmax/dt

But I truly don't know how to achieve all the details about codes and I m asking help here. Hoping you guys can show your hands and thanks for that so much!!!!