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discrete & continuous nonlinear dynamics 301x10.8Entropy0.5λ0.400–0.5–0.4Lyapunov exponent3 3.2 3.4 3.6 3.8 4µ3.5 3.6 3.7 3.8 3.9 4µFigure 12.4 Left: Lyapunov exponent and bifurcation values for the logistic map as functionsof the growth rate µ. Right: Shannon entropy (reduced by a factor of 5) and the Lyapunovcoefficient for the logistic map.✞2. Consider the tent map. Rather than compute this map, study it with just a pieceof paper.a. Make sketches of what a graph of population x i versus generation number iwould look like for extinction, for a period-one cycle, and for a period-twocycle.b. Show that there is a single fixed point for µ>1/2 and a period-two cyclefor µ>1./ / Entropy . java , Shannon entropy of logistic mapimport java . io .∗ ;import java . util .∗ ;public class Entropy {☎✝}public static void main ( String [] argv ) throws IOException , FileNotFoundException {PrintWriter w = new PrintWriter (new FileOutputStream ("Entropy . dat") , true );double prob [] = new double [1001]; //Probabilitiesint nbin = 1000, nmax = 100000, j , n, ibin ;double entropy , x , mu;System . out . println ("Entropy output in Entropy . dat") ;for ( mu = 3.5; mu