Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use Model
This paper is devoted to studying the mathematical model of the alcohol-consuming population. For this purpose, the formulation of the model including the alcohol-consuming population is presented; then the balance points related to non-alcohol use and positive alcohol use are discussed. Hurwitz the...
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| Format: | Article |
| Language: | English |
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Sakarya University
2021-12-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/1818202 |
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| author | Ömer Faruk Gözükızıl Recai Tarakçı |
| author_facet | Ömer Faruk Gözükızıl Recai Tarakçı |
| author_sort | Ömer Faruk Gözükızıl |
| collection | DOAJ |
| description | This paper is devoted to studying the mathematical model of the alcohol-consuming population. For this purpose, the formulation of the model including the alcohol-consuming population is presented; then the balance points related to non-alcohol use and positive alcohol use are discussed. Hurwitz theorem is used to find the local stability of the model, and Lyapunov function theory is used to investigate the global stability. The same mathematical model with alcohol use is considered for Sakarya and Turkey, individual numerical results are presented, and stability analyzes are examined. Finally, using the numerical data, a simulation is made in Matlab with the Runge-Kutta fourth-order method. |
| format | Article |
| id | doaj-art-993f88bcd56342848c27aef88a68386d |
| institution | Kabale University |
| issn | 2147-835X |
| language | English |
| publishDate | 2021-12-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-993f88bcd56342848c27aef88a68386d2024-12-23T08:08:56ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2021-12-012561332134210.16984/saufenbilder.95087828Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use ModelÖmer Faruk Gözükızıl0https://orcid.org/0000-0002-5975-6430Recai Tarakçı1https://orcid.org/0000-0001-7569-8974SAKARYA ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİSAKARYA ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ, MATEMATİK (YL) (TEZLİ)This paper is devoted to studying the mathematical model of the alcohol-consuming population. For this purpose, the formulation of the model including the alcohol-consuming population is presented; then the balance points related to non-alcohol use and positive alcohol use are discussed. Hurwitz theorem is used to find the local stability of the model, and Lyapunov function theory is used to investigate the global stability. The same mathematical model with alcohol use is considered for Sakarya and Turkey, individual numerical results are presented, and stability analyzes are examined. Finally, using the numerical data, a simulation is made in Matlab with the Runge-Kutta fourth-order method.https://dergipark.org.tr/tr/download/article-file/1818202alcohol use modeldifferential equation systemstability analysisequilibrium model of the mathematical model |
| spellingShingle | Ömer Faruk Gözükızıl Recai Tarakçı Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use Model Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi alcohol use model differential equation system stability analysis equilibrium model of the mathematical model |
| title | Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use Model |
| title_full | Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use Model |
| title_fullStr | Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use Model |
| title_full_unstemmed | Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use Model |
| title_short | Examination of Stability Analysis of Sakarya and Turkey Scale Alcohol Use Model |
| title_sort | examination of stability analysis of sakarya and turkey scale alcohol use model |
| topic | alcohol use model differential equation system stability analysis equilibrium model of the mathematical model |
| url | https://dergipark.org.tr/tr/download/article-file/1818202 |
| work_keys_str_mv | AT omerfarukgozukızıl examinationofstabilityanalysisofsakaryaandturkeyscalealcoholusemodel AT recaitarakcı examinationofstabilityanalysisofsakaryaandturkeyscalealcoholusemodel |