Local stabilization and network synchronization: The case of stationary regimes
Relationships between local stability and synchronization in networks of identical dynamical systems are established through the Master Stability Function approach. First, it is shown that stable equilibria of the local dynamics correspond to stable stationary synchronous regimes of the entire netw...
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AIMS Press
2010-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.623 |
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| _version_ | 1832590229890924544 |
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| author | Stefano Fasani Sergio Rinaldi |
| author_facet | Stefano Fasani Sergio Rinaldi |
| author_sort | Stefano Fasani |
| collection | DOAJ |
| description | Relationships between local stability and synchronization in networks of identical dynamical systems are established through the Master Stability Function approach. First, it is shown that stable equilibria of the local dynamics correspond to stable stationary synchronous regimes of the entire network if the coupling among the systems is sufficiently weak or balanced (in other words, stationary synchronous regimes can be unstable only if the coupling is sufficiently large and unbalanced). Then, it is shown that [de]stabilizing factors at local scale are [de]synchronizing at global scale again if the coupling is sufficiently weak or balanced. These results allow one to transfer, with almost no effort, what is known for simple prototypical models in biology and engineering to complex networks composed of these models. This is shown through a series of applications ranging from networks of electrical circuits to various problems in ecology and sociology involving migrations of plants, animal and human populations. |
| format | Article |
| id | doaj-art-f3ff6408e69f4d69b3a3a82eb13da2b9 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f3ff6408e69f4d69b3a3a82eb13da2b92025-01-24T02:00:43ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-05-017362363910.3934/mbe.2010.7.623Local stabilization and network synchronization: The case of stationary regimesStefano Fasani0Sergio Rinaldi1DEI, Politecnico di Milano Via Ponzio 34/5 20133 MilanoDEI, Politecnico di Milano Via Ponzio 34/5 20133 MilanoRelationships between local stability and synchronization in networks of identical dynamical systems are established through the Master Stability Function approach. First, it is shown that stable equilibria of the local dynamics correspond to stable stationary synchronous regimes of the entire network if the coupling among the systems is sufficiently weak or balanced (in other words, stationary synchronous regimes can be unstable only if the coupling is sufficiently large and unbalanced). Then, it is shown that [de]stabilizing factors at local scale are [de]synchronizing at global scale again if the coupling is sufficiently weak or balanced. These results allow one to transfer, with almost no effort, what is known for simple prototypical models in biology and engineering to complex networks composed of these models. This is shown through a series of applications ranging from networks of electrical circuits to various problems in ecology and sociology involving migrations of plants, animal and human populations.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.623dynamical systemsmaster stability function.population dynamicssynchronizing factorsnetworksstabilizing factorssynchronization |
| spellingShingle | Stefano Fasani Sergio Rinaldi Local stabilization and network synchronization: The case of stationary regimes Mathematical Biosciences and Engineering dynamical systems master stability function. population dynamics synchronizing factors networks stabilizing factors synchronization |
| title | Local stabilization and network synchronization: The case of stationary regimes |
| title_full | Local stabilization and network synchronization: The case of stationary regimes |
| title_fullStr | Local stabilization and network synchronization: The case of stationary regimes |
| title_full_unstemmed | Local stabilization and network synchronization: The case of stationary regimes |
| title_short | Local stabilization and network synchronization: The case of stationary regimes |
| title_sort | local stabilization and network synchronization the case of stationary regimes |
| topic | dynamical systems master stability function. population dynamics synchronizing factors networks stabilizing factors synchronization |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.623 |
| work_keys_str_mv | AT stefanofasani localstabilizationandnetworksynchronizationthecaseofstationaryregimes AT sergiorinaldi localstabilizationandnetworksynchronizationthecaseofstationaryregimes |