Coarse Dynamics for Coarse Modeling: An Example From Population Biology
Networks have become a popular way to concisely represent complex nonlinear systems where the interactions and parameters are imprecisely known. One challenge is how best to describe the associated dynamics, which can exhibit complicated behavior sensitive to small changes in parameters. A recently...
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| Format: | Article |
| Language: | English |
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MDPI AG
2014-06-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/16/6/3379 |
| _version_ | 1828117203872907264 |
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| author | Justin Bush Konstantin Mischaikow |
| author_facet | Justin Bush Konstantin Mischaikow |
| author_sort | Justin Bush |
| collection | DOAJ |
| description | Networks have become a popular way to concisely represent complex nonlinear systems where the interactions and parameters are imprecisely known. One challenge is how best to describe the associated dynamics, which can exhibit complicated behavior sensitive to small changes in parameters. A recently developed computational approach that we refer to as a database for dynamics provides a robust and mathematically rigorous description of global dynamics over large ranges of parameter space. To demonstrate the potential of this approach we consider two classical age-structured population models that share the same network diagram and have a similar nonlinear overcompensatory term, but nevertheless yield different patterns of qualitative behavior as a function of parameters. Using a generalization of these models we relate the different structure of the dynamics that are observed in the context of biologically relevant questions such as stable oscillations in populations, bistability, and permanence. |
| first_indexed | 2024-04-11T13:10:25Z |
| format | Article |
| id | doaj.art-7a6cbd7d6fba407788b49c66eb37c41e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:10:25Z |
| publishDate | 2014-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-7a6cbd7d6fba407788b49c66eb37c41e2022-12-22T04:22:36ZengMDPI AGEntropy1099-43002014-06-011663379340010.3390/e16063379e16063379Coarse Dynamics for Coarse Modeling: An Example From Population BiologyJustin Bush0Konstantin Mischaikow1Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway, NJ 08854, USADepartment of Mathematics and BioMaPS, Hill Center-Busch Campus, Rutgers, The State Universityof New Jersey, 110 Frelinghuysen Rd, Piscataway, NJ 08854, USANetworks have become a popular way to concisely represent complex nonlinear systems where the interactions and parameters are imprecisely known. One challenge is how best to describe the associated dynamics, which can exhibit complicated behavior sensitive to small changes in parameters. A recently developed computational approach that we refer to as a database for dynamics provides a robust and mathematically rigorous description of global dynamics over large ranges of parameter space. To demonstrate the potential of this approach we consider two classical age-structured population models that share the same network diagram and have a similar nonlinear overcompensatory term, but nevertheless yield different patterns of qualitative behavior as a function of parameters. Using a generalization of these models we relate the different structure of the dynamics that are observed in the context of biologically relevant questions such as stable oscillations in populations, bistability, and permanence.http://www.mdpi.com/1099-4300/16/6/3379database for dynamicsconley theorypopulation model |
| spellingShingle | Justin Bush Konstantin Mischaikow Coarse Dynamics for Coarse Modeling: An Example From Population Biology Entropy database for dynamics conley theory population model |
| title | Coarse Dynamics for Coarse Modeling: An Example From Population Biology |
| title_full | Coarse Dynamics for Coarse Modeling: An Example From Population Biology |
| title_fullStr | Coarse Dynamics for Coarse Modeling: An Example From Population Biology |
| title_full_unstemmed | Coarse Dynamics for Coarse Modeling: An Example From Population Biology |
| title_short | Coarse Dynamics for Coarse Modeling: An Example From Population Biology |
| title_sort | coarse dynamics for coarse modeling an example from population biology |
| topic | database for dynamics conley theory population model |
| url | http://www.mdpi.com/1099-4300/16/6/3379 |
| work_keys_str_mv | AT justinbush coarsedynamicsforcoarsemodelinganexamplefrompopulationbiology AT konstantinmischaikow coarsedynamicsforcoarsemodelinganexamplefrompopulationbiology |