The heart beat rate has to be well regulated to provide enough oxygenated blood throughout the body and so depends on feedback with the body’s oxygen demand. A simple discrete model of heart beat regulation is given by: xt+1 = kxt(1 - xt) Here xt represents the normalised heart beat rate at time t recorded once per minute. That is, the normalisation involves dividing the actual hear rate in beats per minute by 80 beats per minute. The parameter k is a positive real number (hopefully) greater than 0. (a) Assuming k = 1 what are the steady state solutions (also known as fixed points) for xt? That is, when xt+1 = xt (b) Assuming k = 2 what are the fixed points? (c) Write a MATLAB program using array operations to generate a table (with headings) of the normalised heart beat rate per minute starting at time t = 0 with the value of x0 entered by the user. Run your program with the maximum time set to 30 minutes. Show table and MATLAB code for x0 = 0.1 and k = 2
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x=0.1; beats=A(1,30); for k=1:30 A=2x*(1-x); x=A; disp(A) end