Periodic solution of a bioeconomic fishery model by coincidence degree theory
In this article we use coincidence degree theory to study the existence of a positive periodic solutions to the following bioeconomic model in fishery dynamics \begin{equation*}\label{eq1.3} \begin{cases} \frac{dn}{dt} = n \left(r(t) \left(1-\frac{n}{K}\right)-\frac{q(t)E}{n+D}\right),\\ \frac{...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2023-08-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10416 |
| Summary: | In this article we use coincidence degree theory to study the existence of a positive periodic solutions to the following bioeconomic model in fishery dynamics
\begin{equation*}\label{eq1.3}
\begin{cases}
\frac{dn}{dt} = n \left(r(t) \left(1-\frac{n}{K}\right)-\frac{q(t)E}{n+D}\right),\\
\frac{dE}{dt} = E\left(\frac{A(t)q(t)}{\alpha(t)} \frac{n}{n+D}-\frac{q^2(t)}{\alpha(t)} \frac{n^2E}{(n+D)^2}-c(t)\right),
\end{cases}
\end{equation*}
where the functions $r,q,A,c$ and $\alpha$ are continuous positive $T$-periodic functions. This is the model of a coastal fishery represented as a single site with $n(t)$ is the fish stock biomass, and $E(t)$ is the fishing effort. Examples are given to strengthen our results. |
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| ISSN: | 1417-3875 |