Please show work Consider the following non-linear pairs of equations (i.e. syst
ID: 2883737 • Letter: P
Question
Please show work
Consider the following non-linear pairs of equations (i.e. systems), x' = -x + xy = f(x, y) > y' = 2y - y^2 _ Xy = g(x, y). Which species a- or y is the prey? If the number of predators were to vanish, what equation would the prey satisfy? What are the equilibrium points of this equation? Classify them. Find ail the equilibrium points for the full non-linear system. The two species CAN coexist. At what levels (x_co, y_co).? Linearize the system about this point by using the change of variables u = x - x_co and upsilon - y - y_co. Now. by classifying the linearized system, decide whether stable coexistence is really possible for this pair of species over teh long term. Returning back to the original system at the top of the page, compute the Jacobian J = (f_x f_y g_x g_y) Finally, substitute {x_co. y_co) into J in h), and let A = J(x_co, y_co). Now proceed as in 1): D =, T =, T^2/A =, Type =.Explanation / Answer
given the systems x' = -x+xy and y' = 2y -y^2 -xy
a) f(x,y) denotes the prey
b) for the predetors to be extinct it should satisfy x =0
c) now the condtions x'= 0 and y' = 0
=> x(-1+y) = 0 => x =0 and y = 1
and y(2-y-x) = 0 => y= 0 and x = 2
the equilibrium points are (0,1) and (0,2)