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  3. 2 consider the survival of a population of whales and...

Question: 2 consider the survival of a population of whales and...

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2. Consider the survival of a population of whales, and assume that if the number of whales falls below a minimum survival level m, then the species will become extinct. In addition assume that the population is limited by the carrying capacity M of the environment. That is, if the whale population is above M, then it will experience a decline because the environment cannot sustain that large a population level a) Let an represent the whale population after n years. Consider the model an+1 an +k(M-an)(an m), where k > 0. Describe the model: what are the variables, the parameters, what does each term mean. Does this model fit the description above? that M 5000, m100, and k 0.0001 results from b)? b) Find the fixed points of the model, and describe their stability via linearization. Assume c) Perform a graphical stability analysis using cobwebbing. Are your results consistent with the d) Sketch the graphs of an versus n for various representative initial conditions e) This model fails when the initial population size ao is too small or too large. Why?

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