Find the jacobian j(p+)

Graph the characteristic polynomial for four choices of r

Exercise 4: Let P+ = (n, 77, r 1), where 77 = Ugh 1). Find the Jaco- bian J(P+). The characteristic polynomial of this is p()\\) = det(J(P+) AI) = )\\3 % A2 %(r + 10))\\ + @(1 r). Graph the characteristic polynomial for four choices of r: one in the interval (1.1.34562), one with r = 1.34562, one in the interval (1.34562,24.7368), and one with r > 24.7368. Use your graphs to determine the type and stability of the critical point in the first three cases. Is it obvious what is happening when r > 24.7368? (The values r = 1.34562 and r = 24.7368 are those where significant changes in the behavior of the system occur.3) Describe what properties of the critical point you can see changing as r crosses these values