Question

I hope you find humor behind my teacher's strange imagination. I understand a and b, but had trouble finishing the problem. Any help appreciated, thanks!

7. [27 points A pet store wants to start selling radioactive fish. These come in two typesfour-eyed, and six-eyed, as shown. Let r(t) denote the population of four-eyed fish, and y(t) the population of six-eyed fish. Since the fish will be kept in the same tank, they will fight each other. However, the pet store will receive some new fish of both types each week, so the local ichthyologist (a dude or dudette who studies fish) has determined that r and y are governed by the following system of differential equations 3.8 2.4y 13 dt -2.4 2y +1 dt a) Is the system i. autonomous? yes ii. inear? yesno iii homogeneous? yes no b) Find the equilibrium point (r*,y*) Get the algebra right, or it breaks the rest of the problem. The coordinates are integers. dr 82++2+1 dt dt c) Make the change of variable u = x-x*, u = y-y*. Solve the resulting system. ( The characteristic polynomial is X2 4-5 .) d) Sketch the phase portrait for (Only the part in the first quadrant is necessary.) Use your phase portrait (not algebra) to determine what will happen to the two populations if the pet store makes an initial order of... ·Mo = 5 six-eyed fish and no four-eyed fish. ·Yo = 4 six-eyed fish and no four-eyed fish.

Answer 1

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