Equilibrium solutions for microscopic stochastic systems in population dynamics
The present paper deals with the problem of existence of equilibrium solutionsof equations describing the general population dynamics at the microscopic levelof modified Liouville equation (individually--based model) corresponding to a Markovjump process. We show the existence of factorized equilibr...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.777 |
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| _version_ | 1832590105489965056 |
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| author | MirosŁaw Lachowicz Tatiana Ryabukha |
| author_facet | MirosŁaw Lachowicz Tatiana Ryabukha |
| author_sort | MirosŁaw Lachowicz |
| collection | DOAJ |
| description | The present paper deals with the problem of existence of equilibrium solutionsof equations describing the general population dynamics at the microscopic levelof modified Liouville equation (individually--based model) corresponding to a Markovjump process. We show the existence of factorized equilibrium solutions and discussuniqueness. The conditions guaranteeing uniqueness or non-uniqueness are proposedunder the assumption of periodic structures. |
| format | Article |
| id | doaj-art-2b2dff42c8ec4cc5ac514061ffc2c056 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2b2dff42c8ec4cc5ac514061ffc2c0562025-01-24T02:26:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-03-0110377778610.3934/mbe.2013.10.777Equilibrium solutions for microscopic stochastic systems in population dynamicsMirosŁaw Lachowicz0Tatiana Ryabukha1Institute of Applied Mathematics and Mechanics, University of Warsaw, 2, Banach Str., 02-097 WarsawInstitute of Applied Mathematics and Mechanics, University of Warsaw, 2, Banach Str., 02-097 WarsawThe present paper deals with the problem of existence of equilibrium solutionsof equations describing the general population dynamics at the microscopic levelof modified Liouville equation (individually--based model) corresponding to a Markovjump process. We show the existence of factorized equilibrium solutions and discussuniqueness. The conditions guaranteeing uniqueness or non-uniqueness are proposedunder the assumption of periodic structures.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.777markow jump processpopulation dynamicsmicroscopic modelsintegro-differential equations. |
| spellingShingle | MirosŁaw Lachowicz Tatiana Ryabukha Equilibrium solutions for microscopic stochastic systems in population dynamics Mathematical Biosciences and Engineering markow jump process population dynamics microscopic models integro-differential equations. |
| title | Equilibrium solutions for microscopic stochastic systems in population dynamics |
| title_full | Equilibrium solutions for microscopic stochastic systems in population dynamics |
| title_fullStr | Equilibrium solutions for microscopic stochastic systems in population dynamics |
| title_full_unstemmed | Equilibrium solutions for microscopic stochastic systems in population dynamics |
| title_short | Equilibrium solutions for microscopic stochastic systems in population dynamics |
| title_sort | equilibrium solutions for microscopic stochastic systems in population dynamics |
| topic | markow jump process population dynamics microscopic models integro-differential equations. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.777 |
| work_keys_str_mv | AT mirosławlachowicz equilibriumsolutionsformicroscopicstochasticsystemsinpopulationdynamics AT tatianaryabukha equilibriumsolutionsformicroscopicstochasticsystemsinpopulationdynamics |