One of the following vector Sold plow corresponds to the sys

One of the following vector Sold plow corresponds to the system x\'(t) = 1 - x^2 - y^2, y\'(t) = x^2 - y^2 with the solid circle tracing the x\' = 0 nullcline and the dashed lines tracing the y\' = 0 nulkline. Determine which of the plots is correct Justify your answer by identifying at least one wrong feature for each incorrect plot.

Solution

(c) represents the correct plot

(a) is ruled out because on the x axis , the vector field should be oriented along the xaxis/

(b) is ruled out because on the x-axis, the direction in the plot is opposite to the x-axis

(d) is ruled out , as in the region x>y, the direction of the vector field is wrong.(both x\' and y\' should be positive, so the direction field should make an acute angle with the positive direction of the xaxis

(c) represents the correct plot