Positive role of multiplication noise in attaining complete synchronization on large complex networks of dynamical systems
•The dynamical networks with complex structure are investigated.•The condition of synchronization is acquired by theoretical analyses.•Theoretical result shows noise plays a positive role in attaining synchronization.•The key role of eigenvalues of coupling matrix in attaining synchronization is rev...
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| Veröffentlicht in: | Applied Mathematical Modelling 2018-02, Vol.54, p.803-816 |
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| creator | Xiao, Yuzhu Tang, Sufang Sun, Zhongkui Song, Xueli |
| description | •The dynamical networks with complex structure are investigated.•The condition of synchronization is acquired by theoretical analyses.•Theoretical result shows noise plays a positive role in attaining synchronization.•The key role of eigenvalues of coupling matrix in attaining synchronization is revealed.
In this paper, the role of multiplicative noise in attaining complete synchronization on large complex networks of dynamical systems is investigated by theoretical analysis and numerical simulations. Based on the stability theory of stochastic differential equation, we prove that the multiplicative noise plays a positive role in attaining synchronization if the complex networks of dynamical systems are bounded. Moreover, the theoretical result shows that smaller second eigenvalue of coupling matrix is of benefit in attaining complete synchronization. To demonstrate the correctness of theoretical results, the coupled Lorenz systems, Hindmarsh–Rose neuronal systems and Rössler-like systems are performed as numerical examples. |
| doi_str_mv | 10.1016/j.apm.2017.09.035 |
| format | Article |
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In this paper, the role of multiplicative noise in attaining complete synchronization on large complex networks of dynamical systems is investigated by theoretical analysis and numerical simulations. Based on the stability theory of stochastic differential equation, we prove that the multiplicative noise plays a positive role in attaining synchronization if the complex networks of dynamical systems are bounded. Moreover, the theoretical result shows that smaller second eigenvalue of coupling matrix is of benefit in attaining complete synchronization. To demonstrate the correctness of theoretical results, the coupled Lorenz systems, Hindmarsh–Rose neuronal systems and Rössler-like systems are performed as numerical examples.</description><identifier>ISSN: 0307-904X</identifier><identifier>ISSN: 1088-8691</identifier><identifier>EISSN: 0307-904X</identifier><identifier>DOI: 10.1016/j.apm.2017.09.035</identifier><language>eng</language><publisher>New York: Elsevier Inc</publisher><subject>Chaos ; Computer simulation ; Differential equations ; Dynamical network ; Dynamical systems ; Eigenvalues ; Lorenz system ; Networks ; Noise ; Noise-induced synchronization ; Stability analysis ; Stochastic models ; Studies ; Synchronism</subject><ispartof>Applied Mathematical Modelling, 2018-02, Vol.54, p.803-816</ispartof><rights>2017 Elsevier Inc.</rights><rights>Copyright Elsevier BV Feb 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-2fc760ef57ea1d8df54fb1aaa8fa6ffcb29a33b84af1909e3a5249dce965ee6f3</citedby><cites>FETCH-LOGICAL-c325t-2fc760ef57ea1d8df54fb1aaa8fa6ffcb29a33b84af1909e3a5249dce965ee6f3</cites><orcidid>0000-0002-0664-5403</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.apm.2017.09.035$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3548,27923,27924,45994</link.rule.ids></links><search><creatorcontrib>Xiao, Yuzhu</creatorcontrib><creatorcontrib>Tang, Sufang</creatorcontrib><creatorcontrib>Sun, Zhongkui</creatorcontrib><creatorcontrib>Song, Xueli</creatorcontrib><title>Positive role of multiplication noise in attaining complete synchronization on large complex networks of dynamical systems</title><title>Applied Mathematical Modelling</title><description>•The dynamical networks with complex structure are investigated.•The condition of synchronization is acquired by theoretical analyses.•Theoretical result shows noise plays a positive role in attaining synchronization.•The key role of eigenvalues of coupling matrix in attaining synchronization is revealed.
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| ispartof | Applied Mathematical Modelling, 2018-02, Vol.54, p.803-816 |
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| subjects | Chaos Computer simulation Differential equations Dynamical network Dynamical systems Eigenvalues Lorenz system Networks Noise Noise-induced synchronization Stability analysis Stochastic models Studies Synchronism |
| title | Positive role of multiplication noise in attaining complete synchronization on large complex networks of dynamical systems |
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