Mudassir Lodi

Homework for Lecture 8 of Dr. Z.’s Dynamical Models in Biology class
Email the answers (either as .pdf file or .txt file) to ShaloshBEkhad@gmail.com by 8:00pm Monday, Oct. 4,, 2021. Subject: hw8 with an attachment hw8FirstLast.pdf and/or hw8FirstLast.txt
Also please indicate (EITHER way) whether it is OK to post

1.	Let ai be the i-th digit of your RUID. If it is 0 make it 1. Define a function
	 	.
Use Maple to find the first 1000 terms of the non-linear recurrence
	xn = f(xn−1)	,x0 = 1	.
Is there a steady state? If there is, can you find it exactly? Is it stable?
f(x) = (2 + x)/(1+x)
f:=(2+x)/(1+x)
evalf(Orb(f, x, 1, 0, 1000))
f’(x) = -1/(x+1)^2
f’(0) = -1
There is one stable fixed point, -1. 

2.	Find the first 1000 terms of the orbit starting at x0 = 0.5 of the recurrence
	xn = kxn−1(1 − xn−1)	,
for k = 1, k = 2, k = 2.5, k = 3.1, k = 3.5. What do you find?

f:= x(1-x), 2x(1-x), 2.5x(1-x), 3.1x(1-x), 3.5x(1-x)
evalf(Orb(f,x,0.5,0,1000))
All listed k coefficients would result in stable fixed points. 

3.	Let ai be the i-th digit of your RUID. If it is 0 make it 1. Find the first 1000 terms of the
non-linear second-order recurrence, with the given initial conditions
 .
Is there a steady state?
x(n) = (2x(n-1) + x(n-2))/(x(n-1)+2x(n-2))
Orb(x(n), 0.5, 0.7, 0, 1000)