Relations between the dynamics of network systems and their subnetworks
Statistical analysis of the connectivity of real world networks have revealed interesting featuressuch as community structure, network motif and as on. Such discoveries tempt us to understandthe dynamics of a complex network system by studying those of its subnetworks. This approach isfeasible only...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/10.3934/Math.2017.2.437/fulltext.html |
| _version_ | 1828839193645678592 |
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| author | YunjiaoWang Kiran Chilakamarri Demetrios Kazakos Maria C. Leite |
| author_facet | YunjiaoWang Kiran Chilakamarri Demetrios Kazakos Maria C. Leite |
| author_sort | YunjiaoWang |
| collection | DOAJ |
| description | Statistical analysis of the connectivity of real world networks have revealed interesting featuressuch as community structure, network motif and as on. Such discoveries tempt us to understandthe dynamics of a complex network system by studying those of its subnetworks. This approach isfeasible only if the dynamics of the subnetwork systems can somehow be preserved or partially preservedin the whole system. Most works studied the connectivity structures of networks while very fewconsidered the possibility of translating the dynamics of a subnetwork system to the whole system. Inthis paper, we address this issue by focusing on considering the relations between cycles and fixedpoints of a network system and those of its subnetworks based on Boolean framework. We proved thatat a condition we called agreeable, if X0 is a fixed point of the whole system, then X<sub>0</sub> restricted to thephase-space of one of the subnetwork systems must be a fixed point as well. An equivalent statementon cycles follows from this result. In addition, we discussed the relations between the product of thetransition diagrams (a representation of trajectories) of subnetwork systems and the transition diagramof the whole system. |
| first_indexed | 2024-12-12T19:18:18Z |
| format | Article |
| id | doaj.art-78f63d4dbe924f258c5e43e6f28a303d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T19:18:18Z |
| publishDate | 2017-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-78f63d4dbe924f258c5e43e6f28a303d2022-12-22T00:14:41ZengAIMS PressAIMS Mathematics2473-69882017-08-012343745010.3934/Math.2017.2.437Relations between the dynamics of network systems and their subnetworksYunjiaoWang0Kiran Chilakamarri1Demetrios Kazakos2Maria C. Leite31 Department of Mathematics, Texas Southern University, 3100 Cleburne, Houston, TX, 77004, USA1 Department of Mathematics, Texas Southern University, 3100 Cleburne, Houston, TX, 77004, USA1 Department of Mathematics, Texas Southern University, 3100 Cleburne, Houston, TX, 77004, USA2 Department of Mathematics, University of South Florida at St. Pete, 140 7th Avenue South St.Petersburg, Florida 33701, USAStatistical analysis of the connectivity of real world networks have revealed interesting featuressuch as community structure, network motif and as on. Such discoveries tempt us to understandthe dynamics of a complex network system by studying those of its subnetworks. This approach isfeasible only if the dynamics of the subnetwork systems can somehow be preserved or partially preservedin the whole system. Most works studied the connectivity structures of networks while very fewconsidered the possibility of translating the dynamics of a subnetwork system to the whole system. Inthis paper, we address this issue by focusing on considering the relations between cycles and fixedpoints of a network system and those of its subnetworks based on Boolean framework. We proved thatat a condition we called agreeable, if X0 is a fixed point of the whole system, then X<sub>0</sub> restricted to thephase-space of one of the subnetwork systems must be a fixed point as well. An equivalent statementon cycles follows from this result. In addition, we discussed the relations between the product of thetransition diagrams (a representation of trajectories) of subnetwork systems and the transition diagramof the whole system.http://www.aimspress.com/article/10.3934/Math.2017.2.437/fulltext.htmlBoolean network systems| cycle| fixed point| subnetwork systems| dynamics |
| spellingShingle | YunjiaoWang Kiran Chilakamarri Demetrios Kazakos Maria C. Leite Relations between the dynamics of network systems and their subnetworks AIMS Mathematics Boolean network systems| cycle| fixed point| subnetwork systems| dynamics |
| title | Relations between the dynamics of network systems and their subnetworks |
| title_full | Relations between the dynamics of network systems and their subnetworks |
| title_fullStr | Relations between the dynamics of network systems and their subnetworks |
| title_full_unstemmed | Relations between the dynamics of network systems and their subnetworks |
| title_short | Relations between the dynamics of network systems and their subnetworks |
| title_sort | relations between the dynamics of network systems and their subnetworks |
| topic | Boolean network systems| cycle| fixed point| subnetwork systems| dynamics |
| url | http://www.aimspress.com/article/10.3934/Math.2017.2.437/fulltext.html |
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