Question

(Problem 3) Consider the following three-species ecosystems: dF F(a – cS) dt ds S(-k + \F – mG) dt dG G(-e+oS). dt Assume that the coefficients are positive constants. Describe the role each species plays in this ecological system. =

Answer 1

Answer:

The given information is

     

dF F(a – c5) $(=k+1F – MG) dt dS dit dG dt Gl-e +05).

In considering the fish without sharks the assumptions concerning polulation growth of the fish ceases at some large population then a logistic growth model might be proposed df = af-bf2 The rate of population change of the fish = 8(F,s) is such that g(7,0) is given by either g(F,0)= af or g(7,0) = af - 172 The latter eqaution incorporates the first if b +0, then there exists an equilibrium II population of fish F= if there are no sharks b The sharks behave in an entirely different manner if there are no fish then the food source of the sharks in nonexistent In this case the death rate of the sharks is expected to exceed the birth rate - Hence in the absence of fish we assume that Fa-cs) To model the growth of fish so the existence od sharks will decrease the growth rate of fish and interaction effect on the growth rate is proportion to the population Consequently the growth rate of the fish a-cs with sharks Where c is this positive proportionality constant S(-k+AF - MG) = G(-e +os)