7. Reconsider the tree problem of Example 5.1. Assume t = 1 /2. (a) Sketch the v

Question

7. Reconsider the tree problem of Example 5.1. Assume t = 1 /2. (a) Sketch the vector field for this model. Indicate the location of eaclh equilibrium in the state space. (b) For each equilibrium point, determine the linear system that approx- imates the behavior of the original dynamical system in the neigh- borhood of the equilibrium point. Write the general solution to this linear system, and sketch the linear phase portrait. (c) Sketch the complete phase portrait for this model, using the results of parts (a) and (b). (d) Suppose that a small number of hardwood trees is introduced into a mature stand of softwood trees. What does our model predict about the future of this forest?

Explanation / Answer

example 5.1 the hardwoods are 10000

the softwoods are 6000

rate o growth is 10%in sofywoods and softwoods are 25%

they both are coexist eachother and the number of hardwoods amd softwoodss are also meet eachother

the increment (in number ) softwoods are 150

and hardwoods are 150

difference is 50

after 80 yeasr they number of softwoods are 18000

and the nummber of hardwoods are 18000

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