Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach
In the famous continuous time random walk (CTRW) model, because of the finite lifetime of biological particles, it is sometimes necessary to temper the power law measure such that the waiting time measure has a convergent first moment. The CTRW model with tempered waiting time measure is the so-call...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/6071412 |
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| author | Weiyuan Ma Changpin Li Jingwei Deng |
| author_facet | Weiyuan Ma Changpin Li Jingwei Deng |
| author_sort | Weiyuan Ma |
| collection | DOAJ |
| description | In the famous continuous time random walk (CTRW) model, because of the finite lifetime of biological particles, it is sometimes necessary to temper the power law measure such that the waiting time measure has a convergent first moment. The CTRW model with tempered waiting time measure is the so-called tempered fractional derivative. In this article, we introduce the tempered fractional derivative into complex networks to describe the finite life span or bounded physical space of nodes. Some properties of the tempered fractional derivative and tempered fractional systems are discussed. Generalized synchronization in two-layer tempered fractional complex networks via pinning control is addressed based on the auxiliary system approach. The results of the proposed theory are used to derive a sufficient condition for achieving generalized synchronization of tempered fractional networks. Numerical simulations are presented to illustrate the effectiveness of the methods. |
| format | Article |
| id | doaj-art-9630b2f5bc224430b527f4f5189d1515 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-9630b2f5bc224430b527f4f5189d15152025-02-03T05:44:46ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/60714126071412Synchronization in Tempered Fractional Complex Networks via Auxiliary System ApproachWeiyuan Ma0Changpin Li1Jingwei Deng2School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaIn the famous continuous time random walk (CTRW) model, because of the finite lifetime of biological particles, it is sometimes necessary to temper the power law measure such that the waiting time measure has a convergent first moment. The CTRW model with tempered waiting time measure is the so-called tempered fractional derivative. In this article, we introduce the tempered fractional derivative into complex networks to describe the finite life span or bounded physical space of nodes. Some properties of the tempered fractional derivative and tempered fractional systems are discussed. Generalized synchronization in two-layer tempered fractional complex networks via pinning control is addressed based on the auxiliary system approach. The results of the proposed theory are used to derive a sufficient condition for achieving generalized synchronization of tempered fractional networks. Numerical simulations are presented to illustrate the effectiveness of the methods.http://dx.doi.org/10.1155/2019/6071412 |
| spellingShingle | Weiyuan Ma Changpin Li Jingwei Deng Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach Complexity |
| title | Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach |
| title_full | Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach |
| title_fullStr | Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach |
| title_full_unstemmed | Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach |
| title_short | Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach |
| title_sort | synchronization in tempered fractional complex networks via auxiliary system approach |
| url | http://dx.doi.org/10.1155/2019/6071412 |
| work_keys_str_mv | AT weiyuanma synchronizationintemperedfractionalcomplexnetworksviaauxiliarysystemapproach AT changpinli synchronizationintemperedfractionalcomplexnetworksviaauxiliarysystemapproach AT jingweideng synchronizationintemperedfractionalcomplexnetworksviaauxiliarysystemapproach |