Eventual stability properties in a non-autonomous model of population dynamics

We prove that (λ∗,C/λ∗)(λ∗,C/λ∗) is an eventually uniform-asymptotically stable point in the large of the system L̇=C−LG,Ġ=(L−λ(t))G. on the quadrant {(L,G):L≥0,G>0}{(L,G):L≥0,G>0}. Here function λ(t)λ(t) is positive and λ(t)→λ∗>0λ(t)→λ∗>0 as t→∞t→∞. The study was inspired by observations of distributions of peculiar carnivore and herbivore fish species in Lake Tanganyika.