The following autonomous system of differential equations de

The following autonomous system of differential equations describes two populations (measured in thousands) in interaction: x^1 = 5x - x^2 -xy y\' = xy - 2y For each population, describe the type of growth these equations suggest the population would follow in the absence of the other population. Explain your answers What sort of interaction (predator - pray completion co-operation) does this model show If appropriate explain the role if each population in this intreaction.

Solution

Y\' = (X-2) Y

Y\' < 0 if X<2 and Y\'>0 if X > 2

and Y\' increases if Y increases

the population of Y will increase till it becomes constant

X\' = X(-X + (5-Y))

X\' < 0 if X+Y >5

X\' > 0 if X+Y <5

population of X will also increase till t becomes constant.

If X < 2, Y population will decrease and when X+Y becomes <5 , X poulation will start to increase

It is coperation type of interaction