Homoclinic and heteroclinic solutions to a hepatitis C evolution model
Homoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper. Inverse balancing and generalized differential techniques enable derivatio...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-12-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2018-0130 |
| _version_ | 1818738548123107328 |
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| author | Telksnys Tadas Navickas Zenonas Marcinkevicius Romas Cao Maosen Ragulskis Minvydas |
| author_facet | Telksnys Tadas Navickas Zenonas Marcinkevicius Romas Cao Maosen Ragulskis Minvydas |
| author_sort | Telksnys Tadas |
| collection | DOAJ |
| description | Homoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper. Inverse balancing and generalized differential techniques enable derivation of necessary and sufficient existence conditions for homoclinic/heteroclinic solutions in the considered system. It is shown that homoclinic/heteroclinic solutions do appear when the considered system describes biologically significant evolution. Furthermore, it is demonstrated that the hepatitis C virus evolution model is structurally stable in the topological sense and does maintain homoclinic/heteroclinic solutions as diffusive coupling coefficients tend to zero. Computational experiments are used to illustrate the dynamics of such solutions in the hepatitis C evolution model. |
| first_indexed | 2024-12-18T01:10:41Z |
| format | Article |
| id | doaj.art-c4d03884e6b74e2b9a53406e71b7e8c9 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-18T01:10:41Z |
| publishDate | 2018-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-c4d03884e6b74e2b9a53406e71b7e8c92022-12-21T21:26:06ZengDe GruyterOpen Mathematics2391-54552018-12-011611537155510.1515/math-2018-0130math-2018-0130Homoclinic and heteroclinic solutions to a hepatitis C evolution modelTelksnys Tadas0Navickas Zenonas1Marcinkevicius Romas2Cao Maosen3Ragulskis Minvydas4Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, KaunasLT-51368, LithuaniaResearch Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, KaunasLT-51368, LithuaniaDepartment of Software Engineering, Kaunas University of Technology, Studentu 50-415, KaunasLT-51368, LithuaniaDepartment of Engineering Mechanics, Hohai University, Nanjing210098, ChinaResearch Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, KaunasLT-51368, LithuaniaHomoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper. Inverse balancing and generalized differential techniques enable derivation of necessary and sufficient existence conditions for homoclinic/heteroclinic solutions in the considered system. It is shown that homoclinic/heteroclinic solutions do appear when the considered system describes biologically significant evolution. Furthermore, it is demonstrated that the hepatitis C virus evolution model is structurally stable in the topological sense and does maintain homoclinic/heteroclinic solutions as diffusive coupling coefficients tend to zero. Computational experiments are used to illustrate the dynamics of such solutions in the hepatitis C evolution model.https://doi.org/10.1515/math-2018-0130hepatitis c modelhomoclinic/heteroclinic solutiongeneralized differential operatorinverse balancing34a3435c0792b05 |
| spellingShingle | Telksnys Tadas Navickas Zenonas Marcinkevicius Romas Cao Maosen Ragulskis Minvydas Homoclinic and heteroclinic solutions to a hepatitis C evolution model Open Mathematics hepatitis c model homoclinic/heteroclinic solution generalized differential operator inverse balancing 34a34 35c07 92b05 |
| title | Homoclinic and heteroclinic solutions to a hepatitis C evolution model |
| title_full | Homoclinic and heteroclinic solutions to a hepatitis C evolution model |
| title_fullStr | Homoclinic and heteroclinic solutions to a hepatitis C evolution model |
| title_full_unstemmed | Homoclinic and heteroclinic solutions to a hepatitis C evolution model |
| title_short | Homoclinic and heteroclinic solutions to a hepatitis C evolution model |
| title_sort | homoclinic and heteroclinic solutions to a hepatitis c evolution model |
| topic | hepatitis c model homoclinic/heteroclinic solution generalized differential operator inverse balancing 34a34 35c07 92b05 |
| url | https://doi.org/10.1515/math-2018-0130 |
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