#OK to post homework
#Nicholas DiMarzio, 12/6/21,Assignment 26
#

#P14 ii)
TimeSeries([2*x*(1 - x)*(2 - x)*(3 - x)], [x], [0.01], 0.01, 10, 1)
#We get a horizontal asymtote at x=1 so x=0 is not stable

TimeSeries([2*x*(1 - x)*(2 - x)*(3 - x)], [x], [0.9], 0.01, 10, 1)
#We get a horizontal asymtote at x=1

TimeSeries([2*x*(1 - x)*(2 - x)*(3 - x)], [x], [1.1], 0.01, 10, 1)
#We get a horiztonal asymtote at x =1 so x=1 is stable

TimeSeries([2*x*(1 - x)*(2 - x)*(3 - x)], [x], [2.1], 0.01, 10, 1)
#We get a horiztonal asymtote at x = 3

TimeSeries([2*x*(1 - x)*(2 - x)*(3 - x)], [x], [1.9], 0.01, 10, 1)
#We get a horizontal asymtote at x=1 so x=2 is not stable

TimeSeries([2*x*(1 - x)*(2 - x)*(3 - x)], [x], [2.9], 0.01, 10, 1)
#We get a horizontal asymtote at x= 3

TimeSeries([2*x*(1 - x)*(2 - x)*(3 - x)], [x], [3.1], 0.01, 10, 1)
#We get a horizontal asymtote at x = 3 so x=3 is stable

#P15
Orb([x^3 + 2*y, x^2 + 5*y^2], [x, y], [1, 3], 0, 3);
     [[1, 3], [7, 46], [435, 10629], [82334133, 565067430]]

#P16
F := [(2 + x + y)/(2 + 2*x + 2*y), (2 + x + y)/(1 + 2*x + 2*y)];
                   [  2 + x + y      2 + x + y  ]
              F := [-------------, -------------]
                   [2 + 2 x + 2 y  1 + 2 x + 2 y]

SFP(F, [x, y]);
                 {[0.6953496364, 0.8641637014]}

Orb(F, [x, y], [0.5, 0.4], 1000, 1010);
 [[0.6953496364, 0.8641637013], [0.6953496362, 0.8641637010], 

   [0.6953496365, 0.8641637015], [0.6953496364, 0.8641637013], 

   [0.6953496362, 0.8641637010], [0.6953496365, 0.8641637015], 

   [0.6953496364, 0.8641637013], [0.6953496362, 0.8641637010], 

   [0.6953496365, 0.8641637015], [0.6953496364, 0.8641637013], 

   [0.6953496362, 0.8641637010]]
#P17
TimeSeries([(1 - 2*x - 3*y)*(2 - 2*x - 3*y), (3 - x - 2*y)*(1 - x - 2*y)], [x, y], [-5, 4], 0.01, 10, 1)

#We get a horizaontal line x=-5

TimeSeries([(1 - 2*x - 3*y)*(2 - 2*x - 3*y), (3 - x - 2*y)*(1 - x - 2*y)], [x, y], [-5, 4], 0.01, 10, 2)

#We get a horizontal line y=4

TimeSeries([(1 - 2*x - 3*y)*(2 - 2*x - 3*y), (3 - x - 2*y)*(1 - x - 2*y)], [x, y], [-5.1, 4.1], 0.01, 10, 1)

#The graph blows up to infinity and therefore we have an unstable equilibrium solution

TimeSeries([(1 - 2*x - 3*y)*(2 - 2*x - 3*y), (3 - x - 2*y)*(1 - x - 2*y)], [x, y], [1, 0], 0.01, 10, 1)

#We get a horizatonal line at x=1

TimeSeries([(1 - 2*x - 3*y)*(2 - 2*x - 3*y), (3 - x - 2*y)*(1 - x - 2*y)], [x, y], [1, 0], 0.01, 10, 2)

#We get a horizontal line at y=0

TimeSeries([(1 - 2*x - 3*y)*(2 - 2*x - 3*y), (3 - x - 2*y)*(1 - x - 2*y)], [x, y], [1.1, 0.1], 0.01, 10, 1)

#The graph blows up to infinity thus we have an unstable equilibrium solution