Find the following given predatorprey system Outputs are giv

Find the following given predator/prey system. Outputs are given in thousands/year

R\'(t)= R-2RF

F\'(t)=-0.5F+RF

i) How would you modify prey differential equation given the following factors?

a) The prey migrates away from the area when the number of predators is more than a third that of prey. If the number of predators is less than a third that of prey move into the area.

b) Instead of eating all types of prey the predators only eat the weakest, sickest prey.

ii) How would you modify predator differential equation given the following factors?

a) The predator population becomes more aggressive when hunting prey and as a result, the predator population becomes more successful in killing encountered prey.

b) The predators find a limited food source but they still depend on the prey for their survival.

Solution

i.a)Let k be the rate of migration of preys,

R\'(t)=R-2RF-k(3F-R), if F<R/3 migration is positive,else negative.

b)Let h be the weakest, sickest prey which is proportional to prey.

F\'(t)=-0.5F+hRF.

ii.a)R\'(t)=R-2gRF

b)In the absence of prey, the predators would obey a logistic growth model. Consequently

F\'(t)=kF(1-F/N)+RF