ESPM-EEP%202010%20Lecture%203

ESPM-EEP%202010%20Lecture%203 - ESPM 104/EEP 115 Fall...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ESPM 104/EEP 115 Fall 2010: Lecture 3 1. Cobwebbing analysis of xt +1 = f xt SSG pp. 166 ­171. () 2. The Golden Mean or Ratio: Look at the continued fraction in problem 35 on Page175 (Problem Set, Section 1.7). In this problem the generating sequence equation is for the infinite continued fraction is: 1 an+1 = f an = 1 + an The equilibrium solution is 1 ˆ ˆ ˆ a = 1 + ⇒ a2 − a − 1 = 0 ˆ a 1± 5 ˆ ˆ ⇒a= ⇒ a = −0.618 or 1.618 2 http://en.wikipedia.org/wiki/Golden_ratio 3. Fibonacci’s Rabbits: Look at HISTORICAL QUEST on page 176 of SSG. This is a second order system of difference equations an+1 = an + an−1 It requires two values a0 and a1 to get it started to find a2 () e.g. a0 =1 and a1 =1 implies the sequence: 1, 1, 2, 3, 5, 8, 13, ….. The answer to part c. on page 292 of SSG (Ex 10, Sec. 2.5) illustrates ˆ that the ratio of rabbits in each generation approaches a . 4. Sequential limits SSG Sec. 2.5, p. 275 5. The limit of a sequence is an equilibrium of the generating difference equation SSG Sec. 2.5, p. 281. 6. Discrete Logistic Model SSG p. 284 & Ex 7. 7. Monotone Convergence Theorem: SSG p. 286. 8. Beverton and Holt Sockeye Salmon Dynamics. SSG Ex 8 ...
View Full Document

Ask a homework question - tutors are online