Quiz 03

Please place your name(s) in the upper-right corner.

1. Yesterday we learned how to write loops to iterate processes. Please write, to your best ability, a for loop using R syntax.
   
   
   
   
   
   

2. Please concisely (\(\leq\) 2 sentences) describe the difference between a stable equilibrium and an unstable equilibrium.

3. Which one of the following equilibria does not exist in single-species population models (i.e., one-dimension)?
   A. Oscillatory attractor
   B. Point attractor
   C. Point repeller
   D. Saddle point repeller
   E. Strange attractor

3. For the continuous logistic equations, \(\frac{\mathrm{d}N}{\mathrm{d}t} = N\left(r - \alpha N\right)\), \(\frac{\mathrm{d}N}{\mathrm{d}t} = rN\left(1 - \alpha N\right)\), and \(\frac{\mathrm{d}N}{\mathrm{d}t} = rN\left(\frac{K - N}{K}\right)\), please find the equilibria; i.e., the values of \(N\) where \(\frac{\mathrm{d}N}{\mathrm{d}t} = 0\).
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

4. Please label all equilibria and indicate if each is an attractor (open circle) or repeller (closed circle)?

(So cute)

5. For the following equation, find the equilibria and, as a challenge, plot \(\frac{\mathrm{d}N}{\mathrm{d}t}\) against \(N\): \[\frac{\mathrm{d}N}{\mathrm{d}t} = rN\left(\frac{K-N}{K}\right)\left(\frac{N - A}{A}\right)\]
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

6. Of all of the new terminology you learned in this chapter, which would you use for the name of your band? What genre would it be?