Problem 2: Fishing Models Let x(t) be the population of fish at time t and assume it follows a logistic growth in the absence of fishing with intrinsic growth r > 0 and carrying capacity K > 0. We studied one model in class (model 1) and here we will study two more with two different assumptions: Model 2: assume the harvesting is proportional to the population size: H2x. Model 3: assume the harvesting rate is H3 Air A+x (a) In words, describe the harvesting rate in Model 3. What additional realistic features is it trying to capture? What is the parameter A? (b) Do a phase line analysis of both models, identifying fixed points and stability. (c) Sketch solutions for each model. (See Figure 3.3 or 3.5 in your book for examples). Problem 2: Fishing Models Let x(t) be the population of fish at time t and assume it follows a logistic growth in the absence of fishing with intrinsic growth r > 0 and carrying capacity K > 0. We studied one model in class (model 1) and here we will study two more with two different assumptions: Model 2: assume the harvesting is proportional to the population size: H2x. Model 3: assume the harvesting rate is H3 Air A+x (a) In words, describe the harvesting rate in Model 3. What additional realistic features is it trying to capture? What is the parameter A? (b) Do a phase line analysis of both models, identifying fixed points and stability. (c) Sketch solutions for each model. (See Figure 3.3 or 3.5 in your book for examples)