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Eventual stability properties in a non-autonomous model of population dynamics. (English) Zbl 1204.34064

Author’s abstract: We prove that \((\lambda^{\ast },C/\lambda^{\ast })\) is eventually uniform-asymptotically stable point in the large of the system
\[ \frac{dL}{dt}=C-LG~, \quad \frac{dG}{dt}=(L-\lambda (t))G \]
on the quadrant \(\{(L,G):L\geq 0,G>0\}\) . It holds \(\lambda (t)\rightarrow \lambda^{\ast }>0\) as \(t\rightarrow \infty\). The study is inspired by observations of distributions of peculiar carnivore and herbivore fish species in Lake Tanganyika .

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34D20 Stability of solutions to ordinary differential equations
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References:

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