How to create a function to get bifurcation plot

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!!!!

Answer 1

[Ankitha Kollegal Arjun]

The following MATLAB Answers post might be a useful starting point for your question:

How to create bifurcation diagram

Answer 2

[Yulia Verbitskaya]

m=[0:0.001:2]

A=[0:0.02:3]

for i = 1:length(m)

p(i)=(k3+(k_3*A))./K4*m(i);

MPF_MPF(i)=k1-(k2+k_2*APCon(i)*APCon);

MPF_APCon(i)=(((k3+k_3*A)/k4*m1)*(1-APCon(i))*(K4+APCon(i))/(APCon(i))*(K3+1-APCon(i)));

[cross,index]=min(abs(MPF_MPF-MPF_APCon));

MPF_APCon(i)=MPF_MPF(index);