Assume x1 represents the number of rabbits and x2 represents

Assume x_1 represents the number of rabbits and x2 represents the number of foxes in a forest. The system of differential equations which models this population of rabbits and foxes is given by x1 = Ax where time is measured in years. The eigenvalues and eigenvectors of A are: Sketch the trajectory flow in the first quadrant Use arrows to indicate the direction of the flow as time increases. What happens to the number of rabbits and foxes in the forest if the forest starts out with fewer than 10 rabbits for every fox? Explain. What happens to the number of rabbits and foxes in the forest if the forest starts out with more than 10 rabbits for every fox? Explain. Assume the forest starts out with more than 10 rabbits for every fox. After a long time what will be the ratio of rabbits to foxes? sketch extinction ratio

Solution

(b)here number of rabits are less than to the foxes.so,we can geting more foxes in the forest.we can extent rabits in the forest.

so 10 rabits=20 t0 50 of foxes

(c)here rabits are higher than foxes. here unboundad growth in rabits

its like 50 rabits=10 foxes

(d)the ratio of foxes and rabits are 50;1