Solitary solutions to a metastasis model represented by two systems of coupled Riccati equations
Solitary solutions to a two-tumor metastasis model represented by a system of multiplicatively coupled Riccati equations are considered in this paper. The interaction between tumors is modelled by a one-sided diffusive coupling when one coupled Riccati system influences the other, but not the opposi...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-07-01
|
| Series: | Journal of King Saud University: Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364723001441 |
| _version_ | 1797804699123974144 |
|---|---|
| author | I. Timofejeva T. Telksnys Z. Navickas R. Marcinkevicius R. Mickevicius M. Ragulskis |
| author_facet | I. Timofejeva T. Telksnys Z. Navickas R. Marcinkevicius R. Mickevicius M. Ragulskis |
| author_sort | I. Timofejeva |
| collection | DOAJ |
| description | Solitary solutions to a two-tumor metastasis model represented by a system of multiplicatively coupled Riccati equations are considered in this paper. The interaction between tumors is modelled by a one-sided diffusive coupling when one coupled Riccati system influences the other, but not the opposite. Necessary and sufficient conditions for the existence of solitary solutions to the composite system of Riccati equations are derived in the explicit form. Computational experiments are used to demonstrate the transitions from one steady-state to another via non-monotonous trajectories. |
| first_indexed | 2024-03-13T05:39:59Z |
| format | Article |
| id | doaj.art-dbad9d8c77c74e639428f2f49a064c33 |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-03-13T05:39:59Z |
| publishDate | 2023-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-dbad9d8c77c74e639428f2f49a064c332023-06-14T04:32:49ZengElsevierJournal of King Saud University: Science1018-36472023-07-01355102682Solitary solutions to a metastasis model represented by two systems of coupled Riccati equationsI. Timofejeva0T. Telksnys1Z. Navickas2R. Marcinkevicius3R. Mickevicius4M. Ragulskis5Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania; Corresponding author.Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, LithuaniaCenter for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, LithuaniaDepartment of Software Engineering, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, LithuaniaUrology Clinic, Lithuanian University of Health Sciences, Eiveniu 2, Kaunas LT-50009, LithuaniaCenter for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, LithuaniaSolitary solutions to a two-tumor metastasis model represented by a system of multiplicatively coupled Riccati equations are considered in this paper. The interaction between tumors is modelled by a one-sided diffusive coupling when one coupled Riccati system influences the other, but not the opposite. Necessary and sufficient conditions for the existence of solitary solutions to the composite system of Riccati equations are derived in the explicit form. Computational experiments are used to demonstrate the transitions from one steady-state to another via non-monotonous trajectories.http://www.sciencedirect.com/science/article/pii/S101836472300144135C0834A2592C50 |
| spellingShingle | I. Timofejeva T. Telksnys Z. Navickas R. Marcinkevicius R. Mickevicius M. Ragulskis Solitary solutions to a metastasis model represented by two systems of coupled Riccati equations Journal of King Saud University: Science 35C08 34A25 92C50 |
| title | Solitary solutions to a metastasis model represented by two systems of coupled Riccati equations |
| title_full | Solitary solutions to a metastasis model represented by two systems of coupled Riccati equations |
| title_fullStr | Solitary solutions to a metastasis model represented by two systems of coupled Riccati equations |
| title_full_unstemmed | Solitary solutions to a metastasis model represented by two systems of coupled Riccati equations |
| title_short | Solitary solutions to a metastasis model represented by two systems of coupled Riccati equations |
| title_sort | solitary solutions to a metastasis model represented by two systems of coupled riccati equations |
| topic | 35C08 34A25 92C50 |
| url | http://www.sciencedirect.com/science/article/pii/S1018364723001441 |
| work_keys_str_mv | AT itimofejeva solitarysolutionstoametastasismodelrepresentedbytwosystemsofcoupledriccatiequations AT ttelksnys solitarysolutionstoametastasismodelrepresentedbytwosystemsofcoupledriccatiequations AT znavickas solitarysolutionstoametastasismodelrepresentedbytwosystemsofcoupledriccatiequations AT rmarcinkevicius solitarysolutionstoametastasismodelrepresentedbytwosystemsofcoupledriccatiequations AT rmickevicius solitarysolutionstoametastasismodelrepresentedbytwosystemsofcoupledriccatiequations AT mragulskis solitarysolutionstoametastasismodelrepresentedbytwosystemsofcoupledriccatiequations |