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#### charlottewill

##### New member

- Mar 7, 2012

- 6

dW/dt= αW−βV,

dV/dt= −γV+δW

and the question is as follows:

a) Suppose we have two species interacting on the same environment. After observations we find that the size of their population obey the above set of differential equations where α,β,γ,δ are positive constants.

Determine what variables represents the predators and what variables represent the prey and WHY

b) Solve the system by proposing

W (t) = A sin(ωt) + B cos(ωt)

V (t) = C sin(ωt) + D cos(ωt).

Find the value of the constants A,B,C,D in terms of the parameters α,β,γ,δ ω

There obviously must be a relationship between the equations given in part b) with the main dW/dt dV/dt equations above but how would you answer these questions?