ESPM-EEP%202010%20Lecture%209

ESPM-EEP%202010%20Lecture%209 - ESPM 104/EEP 115 Fall...

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Unformatted text preview: ESPM 104/EEP 115 Fall 2010: Lecture 9 1. Logistic Growth SSG 6.1, pp. 742 ­744. 2. Solution for x(0)=x0: Kx0 ⎛ dx x⎞ = rx ⎜ 1 − ⎟ ⇔ x (t ) = dt ⎝ K⎠ x0 + ( K − x0 )e− rt 3. SSG 6.1 Ex 5. Qualitative Analysis of Logistic Equation dx = f ( x ), x (0) = x0 , SSG 6.5 p. 813. 4. Classifying equilibria of dt dx 5. Linearization and Stability of = f ( x ), x (0) = x0 , SSG 6.5 dt p. 815, Theorem 6.1. 6. SSG 6.5 Ex. 7. Population Resilience. 7. Constant harvesting of logistic model at rate h>0: ⎛ dx x⎞ = rx ⎜ 1 − ⎟ − h dt K⎠ ⎝ See. SSG 6.1, Ex 7. Harvesting Queen Conchs. 8. General harvesting theory of biomass x(t) ODE model : T dx 1 = f ( x ) − h( v , x ), Avg. Yield: Y = ∫ h( v , x )dt dt T0 a. Case 2000, p. 232 ­242. b. Mathematical Bioeconomics. Part II Harvesting Theory Notes. ...
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