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: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2023-08-01
|
| 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 |
| _version_ | 1797352336722493440 |
|---|---|
| author | Satyam Srivastava Seshadev Padhi Alexander Domoshnitsky |
| author_facet | Satyam Srivastava Seshadev Padhi Alexander Domoshnitsky |
| author_sort | Satyam Srivastava |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T13:14:57Z |
| format | Article |
| id | doaj.art-0c675b89e24244499c85185119505516 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-03-08T13:14:57Z |
| publishDate | 2023-08-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-0c675b89e24244499c851851195055162024-01-18T08:28:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752023-08-0120232911210.14232/ejqtde.2023.1.2910416Periodic solution of a bioeconomic fishery model by coincidence degree theorySatyam Srivastava0Seshadev Padhi1Alexander Domoshnitsky2Department of Mathematics, Ariel University, Ariel, IsraelBirla Institute of Technology, Mesra, Ranchi, IndiaAriel University, Ariel, IsraelIn 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10416periodic solutioncoincidence degreeexistence of solution |
| spellingShingle | Satyam Srivastava Seshadev Padhi Alexander Domoshnitsky Periodic solution of a bioeconomic fishery model by coincidence degree theory Electronic Journal of Qualitative Theory of Differential Equations periodic solution coincidence degree existence of solution |
| title | Periodic solution of a bioeconomic fishery model by coincidence degree theory |
| title_full | Periodic solution of a bioeconomic fishery model by coincidence degree theory |
| title_fullStr | Periodic solution of a bioeconomic fishery model by coincidence degree theory |
| title_full_unstemmed | Periodic solution of a bioeconomic fishery model by coincidence degree theory |
| title_short | Periodic solution of a bioeconomic fishery model by coincidence degree theory |
| title_sort | periodic solution of a bioeconomic fishery model by coincidence degree theory |
| topic | periodic solution coincidence degree existence of solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10416 |
| work_keys_str_mv | AT satyamsrivastava periodicsolutionofabioeconomicfisherymodelbycoincidencedegreetheory AT seshadevpadhi periodicsolutionofabioeconomicfisherymodelbycoincidencedegreetheory AT alexanderdomoshnitsky periodicsolutionofabioeconomicfisherymodelbycoincidencedegreetheory |