Dynamics in a Chemotaxis Model with Periodic Source
We consider a system of two differential equations modeling chemotaxis. The system consists of a parabolic equation describing the behavior of a biological species “<i>u</i>” coupled to an ODE patterning the concentration of a chemical substance “<i>v</i>”. The growth of the...
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| Format: | Article |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/312 |
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| author | Mihaela Negreanu Antonio M. Vargas |
| author_facet | Mihaela Negreanu Antonio M. Vargas |
| author_sort | Mihaela Negreanu |
| collection | DOAJ |
| description | We consider a system of two differential equations modeling chemotaxis. The system consists of a parabolic equation describing the behavior of a biological species “<i>u</i>” coupled to an ODE patterning the concentration of a chemical substance “<i>v</i>”. The growth of the biological species is limited by a logistic-like term where the carrying capacity presents a time-periodic asymptotic behavior. The production of the chemical species is described in terms of a regular function <i>h</i>, which increases as “<i>u</i>” increases. Under suitable assumptions we prove that the solution is globally bounded in time by using an Alikakos-Moser iteration, and it fulfills a certain periodic asymptotic behavior. Besides, numerical simulations are performed to illustrate the behavior of the solutions of the system showing that the model considered here can provide very interesting and complex dynamics. |
| first_indexed | 2024-03-09T23:33:31Z |
| format | Article |
| id | doaj.art-c71f9777a9894d449b4a69e3568912fc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:33:31Z |
| publishDate | 2022-01-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c71f9777a9894d449b4a69e3568912fc2023-11-23T17:05:29ZengMDPI AGMathematics2227-73902022-01-0110331210.3390/math10030312Dynamics in a Chemotaxis Model with Periodic SourceMihaela Negreanu0Antonio M. Vargas1Instituto de Matemática Interdisciplinar, Departamento de Análisis Matemático y Matemática Aplicada, UCM, 28040 Madrid, SpainInstituto de Matemática Interdisciplinar, Departamento de Análisis Matemático y Matemática Aplicada, UCM, 28040 Madrid, SpainWe consider a system of two differential equations modeling chemotaxis. The system consists of a parabolic equation describing the behavior of a biological species “<i>u</i>” coupled to an ODE patterning the concentration of a chemical substance “<i>v</i>”. The growth of the biological species is limited by a logistic-like term where the carrying capacity presents a time-periodic asymptotic behavior. The production of the chemical species is described in terms of a regular function <i>h</i>, which increases as “<i>u</i>” increases. Under suitable assumptions we prove that the solution is globally bounded in time by using an Alikakos-Moser iteration, and it fulfills a certain periodic asymptotic behavior. Besides, numerical simulations are performed to illustrate the behavior of the solutions of the system showing that the model considered here can provide very interesting and complex dynamics.https://www.mdpi.com/2227-7390/10/3/312chemotaxisperiodic behaviorglobal existence of solutionsparabolic-ODE systems |
| spellingShingle | Mihaela Negreanu Antonio M. Vargas Dynamics in a Chemotaxis Model with Periodic Source Mathematics chemotaxis periodic behavior global existence of solutions parabolic-ODE systems |
| title | Dynamics in a Chemotaxis Model with Periodic Source |
| title_full | Dynamics in a Chemotaxis Model with Periodic Source |
| title_fullStr | Dynamics in a Chemotaxis Model with Periodic Source |
| title_full_unstemmed | Dynamics in a Chemotaxis Model with Periodic Source |
| title_short | Dynamics in a Chemotaxis Model with Periodic Source |
| title_sort | dynamics in a chemotaxis model with periodic source |
| topic | chemotaxis periodic behavior global existence of solutions parabolic-ODE systems |
| url | https://www.mdpi.com/2227-7390/10/3/312 |
| work_keys_str_mv | AT mihaelanegreanu dynamicsinachemotaxismodelwithperiodicsource AT antoniomvargas dynamicsinachemotaxismodelwithperiodicsource |