In class we introduced the logistic map, which is a simple model for population

Question

In class we introduced the logistic map, which is a simple model for population growth The population in year n is denoted by xn. According to the model, the population is updated according to: Fn+1 = arn(1-1.) Here a is a critical model parameter which governs the transition to chaos in this (i) If you have not already done so, read through section 1.14 of the textbook. Taking = 2.9 and the initial population xi = 0.2, write a program Igmap.m which repro- duces Figure 1.7 in the textbook. You may find the MATLAB commands plot, line, and hold useful for this purpose.

Explanation / Answer

%yn=x(n+1)

syms x;

syms y,i;

syms a=2.9;

x=0.2

for i=1:1:1000

y=a*x(1-x)

plot(y,x)

x=y

end

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