Thread: Char. Eq.

Given:

M = ([0, f_2, f_3], [s_1, 0, 0], [0, s_2, 0])

(Note: [0, f_2, f_3] is the 1st row)

1.) Determine the characterist equation.

2.) Given f_2 = 2, f_3 = 5, s_2 = 0.8, how large must s_1 be to get L >= 1 (L is lambda)

3.) Given f_2 = 2, f_3 = 5, s_1 = 0.2, s_2 = 0.8, determine L with three-decimal-digit accuracy

4.) What's the stable population ratios for the preceding parameter values

I hope I didn't make an error in my calculations, but I got a charpoly of:



If you set the parameters accordingly, when , then

Hmm, yes 1/6 is correct I think, but I don't see how you get it

Originally Posted by flash101

Given:

M = ([0, f_2, f_3], [s_1, 0, 0], [0, s_2, 0])

(Note: [0, f_2, f_3] is the 1st row)

1.) Determine the characterist equation.

2.) Given f_2 = 2, f_3 = 5, s_2 = 0.8, how large must s_1 be to get L >= 1 (L is lambda)

3.) Given f_2 = 2, f_3 = 5, s_1 = 0.2, s_2 = 0.8, determine L with three-decimal-digit accuracy

4.) What's the stable population ratios for the preceding parameter values

The characteristic polynomial is given by the equation:


So we have the matrix


Thus the characteristic polynomial will be given by:




-Dan

How do you get the s_1 = 1/6 though?

Originally Posted by flash101

How do you get the s_1 = 1/6 though?

plug in the given values and solve for s_1. you were given the values of f_2 ...etc in the questions