Species x(t) and y(t) population models are as follows:
ẋ = βx(1 - x/κ) - αxy
ẏ = γxy - δy
(Assuming α,β,γ,κ > 0)
1.) How do the populations behave in the absence of each other?
2.) What type of interaction does the coupling term describe and why?
How do I work out how the populations behave in the absence in each other for q1? Okay so from Benjamin Wang's help I do y=0 which gives me ẋ = βx(1-x/κ) which means the population of x decreases exponentially in the absence of y as (1-x) is going to be negative as x>1. And then in the absence of x where x=0, ẏ= - δy so the population of y decreases exponentially too. So since the population of x and y decreases exponentially in the absence of each other I can say it is co-operation interaction? Is this right?
3.) How would I then calculate all the fixed points and the linear stability of them for this question too?
For 3.) the fixed points I got were (0,0) and (k,0), but are there any more. And how would I calculate the linear stability of these points?
Any help/hints would be much appreciated. Is there any reason why this question isn't being answered