4. In class you discussed a model for fishery management based on the logistic equation with a parameterization of harvesting, N =EN (1-)-mN, N(0) = No where m is the fishing rate ("m" for mortality). With m = 0, there are two fixed points: Ni = 0 (unstable) and N = K (stable). With m > 0, the second fixed point becomes N = K(1 - m/r) K. Thus there are now three fixed points. What are they and which are stable? (c) Now consider m >0 and add the line mN to your graph. Different values of m will lead to different numbers and types of fixed points. Classify the regimes, i.e., make a plot of N* vs. m for each N*, with dotted lines for unstable points, solid lines for stable points (this is called a 'bifurcation diagram'). What is the critcial value of m above which the population dies? What is happening geometrically? Give as complete an analysis as possible