| Contents |
| In this talk we are going to see the asymptotic behaviour of the following prey-predator system
\begin{equation*}
\left\{
\begin{split}
&A'=\alpha f(t)A-\beta g(t)A^2-\gamma AP\\
&P'=\delta h(t)P-\lambda m(t)P^2+\mu AP,
\end{split}
\right.
\end{equation*}
where functions $f,g:\mathbb{R}\rightarrow\mathbb{R}$ are not necessarily bounded above and $f,g,h,m$ can be seen as non-autonomous or random coefficients. I also show the existence of the pullback attractor and the permanence of solutions for any positive initial data and initial time, making a previous study of a logistic equation with unbounded terms, where one of them can be negative for a bounded interval of time. The analysis of a non-autonomous logistic equation with unbounded coefficients is also needed to ensure the permanence of the model. |
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