ESPM-EEP%202010%20Lecture%203

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

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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 ...
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