could anyone please help me with the following problem. A pic of the problem is

Question

could anyone please help me with the following problem. A pic of the problem is attached below.

Computer. This question concerns numerically exploring the solutions of the equation P_n+1 = P_n + 0.1p_n(1 -P_n)(2 -p_n) First determine all the equilibrium solutions of this difference equation. Numerically simulate the difference equation using the following initial conditions p_0 = 0 P_0 = 0.0001 P_0 = .9999 p_0 = 1 P_0 = 1.0001 p_0 = 1.9999 P_0 = 2 P_0 = 2.0001 Describe your results and comment on the stability of the equilibrium you found. Provide plots of all your results. It will make your comparisons easier if

Explanation / Answer

P_n+1 = P_n + 0.1*P_n * (1-P_n)* (2-P_n);

here, original solution is;

P_n =  P_n + 0.1*P_n * (1-P_n)* (2-P_n);

P_n = 0;

P_n = 1;

P_n = 2;

Now, solving on Excel we get;

From solving for Pn we get the following result;

Solution has equilibrium around Pn = 1;

P0 0 0.0001 0.9999 1 1.0001 1.9999 2 2.0001 P1 0 0.0003 1 1 1 1.9997 2 2.0003 P2 0 0.0009 1 1 1 1.9991 2 2.0009 P3 0 0.002696 1 1 1 1.997304 2 2.002704 P4 0 0.008068 1 1 1 1.991932 2 2.008132 P5 0 0.024008 1 1 1 1.975992 2 2.024596 P6 0 0.07031 1 1 1 1.92969 2 2.075619 P7 0 0.196446 1 1 1 1.803554 2 2.244444 P8 0 0.481146 1 1 1 1.518854 2 2.927198 P9 0 0.86032 1 1 1 1.13968 2 8.157792 P10 0 0.997275 1 1 1 1.002725 2 367.7223 P11 0 1 1 1 1 1 2 49318723 P12 0 1 1 1 1 1 2 1.2E+23 P13 0 1 1 1 1 1 2 1.73E+69 P14 0 1 1 1 1 1 2 5.1E+207 P15 0 1 1 1 1 1 2 #NUM! P16 0 1 1 1 1 1 2 #NUM!

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