Question: we have a general predator-prey system, modified so that the prey population has a limit to its growth, is: x'= x(a y x), y'= y(c

we have a general predator-prey system, modified so that the prey population has a limit to its growth, is: x'= x(a y x), y'= y(c + x) where a, c, , , are all positive parameters.

(1) what is the co-existence equilibrium (both populations positive)? and give a condition for its existence.

(2) prove that it is always asymptotically stable when it exists.

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