Question

Consider the following population model:

dx dt =−(x−a)(x−b)

where x(t) is the population density at time t, and a and b are positive constants.

(a) Sketch the phase line for this model.

(b) Use the phase line to identify the fixed points, and indicate the type of stability for each fixed point.

(c) Suppose we add a constant harvest h to this population. Find the critical harvest level (i.e., harvesting above this level results in the population approaching zero for any initial condition).

(d) Suppose we add a percentage harvest hx to this population. Find the critical harvest level (i.e., harvesting above this level results in the population approaching zero for any initial condition).

Answer 1