Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension
In this paper, we introduce a curvilinear coordinate transformation to study the bifurcation of periodic solutions from a 2-degree-of-freedom Hamiltonian system, when it is perturbed in R m + 4 , where m represents any positive integer. The extended Melnikov function is obtained by constructing a Po...
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| Veröffentlicht in: | Journal of nonlinear mathematical physics 2024-04, Vol.31 (1), p.21, Article 21 |
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| creator | Quan, Tingting Li, Jing Sun, Min Chen, Yongqiang |
| description | In this paper, we introduce a curvilinear coordinate transformation to study the bifurcation of periodic solutions from a 2-degree-of-freedom Hamiltonian system, when it is perturbed in
R
m
+
4
, where
m
represents any positive integer. The extended Melnikov function is obtained by constructing a Poincaré map on the curvilinear coordinate frame of the trajectory of the unperturbed system. Then the criteria for bifurcation of periodic solutions of these Hamiltonian systems under isochronous and non-isochronous conditions are obtained. As for its application, we study the number of periodic solutions of a composite piezoelectric cantilever rectangular plate system whose averaged equation can be transformed into a
(
2
+
4
)
-dimensional dynamical system. Furthermore, under the two resonance conditions of 1:1 and 1:2, we obtain the periodic solution numbers of this system with the variation of parametric excitation coefficient
p
1
. |
| doi_str_mv | 10.1007/s44198-024-00181-5 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3031478190</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3031478190</sourcerecordid><originalsourceid>FETCH-LOGICAL-c314t-6a436ecb85146b953c125eb2d32be5343de5806e9eaae14474ecd3f1225297a13</originalsourceid><addsrcrecordid>eNp9kMtKxDAUhoMoOI6-gKuAG0WqubbpUme8wXiB0XVI21PN0CZj0i7m7e1YQVeuzoHz_f-BD6FjSi4oIdllFILmKiFMJIRQRRO5gyY0y9KEKMl2_-z76CDGFSE8S5WaoI9rW_ehNJ31DvsaP_ZNZ9cN4BcI1le2xEvf9NtrxLUP2OBZY2Lcok_eNdaBCXi-caa1pWnwchM7aCO2Dp-25-IsmdsWXBzih2ivNk2Eo585RW-3N6-z-2TxfPcwu1okJaeiS1IjeAploSQVaZFLXlImoWAVZwVILngFUpEUcjAGqBCZgLLiNWVMsjwzlE_Rydi7Dv6zh9jple-DG15qToYXmaI5GSg2UmXwMQao9TrY1oSNpkRvjerRqB6M6m-jWg4hPobiALt3CL_V_6S-ANhZeHw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3031478190</pqid></control><display><type>article</type><title>Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension</title><source>Springer Nature - Complete Springer Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Springer Nature OA Free Journals</source><creator>Quan, Tingting ; Li, Jing ; Sun, Min ; Chen, Yongqiang</creator><creatorcontrib>Quan, Tingting ; Li, Jing ; Sun, Min ; Chen, Yongqiang</creatorcontrib><description>In this paper, we introduce a curvilinear coordinate transformation to study the bifurcation of periodic solutions from a 2-degree-of-freedom Hamiltonian system, when it is perturbed in
R
m
+
4
, where
m
represents any positive integer. The extended Melnikov function is obtained by constructing a Poincaré map on the curvilinear coordinate frame of the trajectory of the unperturbed system. Then the criteria for bifurcation of periodic solutions of these Hamiltonian systems under isochronous and non-isochronous conditions are obtained. As for its application, we study the number of periodic solutions of a composite piezoelectric cantilever rectangular plate system whose averaged equation can be transformed into a
(
2
+
4
)
-dimensional dynamical system. Furthermore, under the two resonance conditions of 1:1 and 1:2, we obtain the periodic solution numbers of this system with the variation of parametric excitation coefficient
p
1
.</description><identifier>ISSN: 1776-0852</identifier><identifier>ISSN: 1402-9251</identifier><identifier>EISSN: 1776-0852</identifier><identifier>DOI: 10.1007/s44198-024-00181-5</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Bifurcations ; Cantilever plates ; Coefficient of variation ; Coordinate transformations ; Dynamical systems ; Fabric analysis ; Hamiltonian functions ; Mathematical Physics ; Mathematics ; Mathematics and Statistics ; Neighborhoods ; Nonlinear systems ; Orbits ; Ordinary differential equations ; Piezoelectricity ; Poincare maps ; Rectangular plates ; Research Article ; Spherical coordinates</subject><ispartof>Journal of nonlinear mathematical physics, 2024-04, Vol.31 (1), p.21, Article 21</ispartof><rights>The Author(s) 2024</rights><rights>Copyright Springer Nature B.V. Dec 2024</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c314t-6a436ecb85146b953c125eb2d32be5343de5806e9eaae14474ecd3f1225297a13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s44198-024-00181-5$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s44198-024-00181-5$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41096,41464,42165,42533,51294,51551</link.rule.ids></links><search><creatorcontrib>Quan, Tingting</creatorcontrib><creatorcontrib>Li, Jing</creatorcontrib><creatorcontrib>Sun, Min</creatorcontrib><creatorcontrib>Chen, Yongqiang</creatorcontrib><title>Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension</title><title>Journal of nonlinear mathematical physics</title><addtitle>J Nonlinear Math Phys</addtitle><description>In this paper, we introduce a curvilinear coordinate transformation to study the bifurcation of periodic solutions from a 2-degree-of-freedom Hamiltonian system, when it is perturbed in
R
m
+
4
, where
m
represents any positive integer. The extended Melnikov function is obtained by constructing a Poincaré map on the curvilinear coordinate frame of the trajectory of the unperturbed system. Then the criteria for bifurcation of periodic solutions of these Hamiltonian systems under isochronous and non-isochronous conditions are obtained. As for its application, we study the number of periodic solutions of a composite piezoelectric cantilever rectangular plate system whose averaged equation can be transformed into a
(
2
+
4
)
-dimensional dynamical system. Furthermore, under the two resonance conditions of 1:1 and 1:2, we obtain the periodic solution numbers of this system with the variation of parametric excitation coefficient
p
1
.</description><subject>Bifurcations</subject><subject>Cantilever plates</subject><subject>Coefficient of variation</subject><subject>Coordinate transformations</subject><subject>Dynamical systems</subject><subject>Fabric analysis</subject><subject>Hamiltonian functions</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Neighborhoods</subject><subject>Nonlinear systems</subject><subject>Orbits</subject><subject>Ordinary differential equations</subject><subject>Piezoelectricity</subject><subject>Poincare maps</subject><subject>Rectangular plates</subject><subject>Research Article</subject><subject>Spherical coordinates</subject><issn>1776-0852</issn><issn>1402-9251</issn><issn>1776-0852</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>BENPR</sourceid><recordid>eNp9kMtKxDAUhoMoOI6-gKuAG0WqubbpUme8wXiB0XVI21PN0CZj0i7m7e1YQVeuzoHz_f-BD6FjSi4oIdllFILmKiFMJIRQRRO5gyY0y9KEKMl2_-z76CDGFSE8S5WaoI9rW_ehNJ31DvsaP_ZNZ9cN4BcI1le2xEvf9NtrxLUP2OBZY2Lcok_eNdaBCXi-caa1pWnwchM7aCO2Dp-25-IsmdsWXBzih2ivNk2Eo585RW-3N6-z-2TxfPcwu1okJaeiS1IjeAploSQVaZFLXlImoWAVZwVILngFUpEUcjAGqBCZgLLiNWVMsjwzlE_Rydi7Dv6zh9jple-DG15qToYXmaI5GSg2UmXwMQao9TrY1oSNpkRvjerRqB6M6m-jWg4hPobiALt3CL_V_6S-ANhZeHw</recordid><startdate>20240403</startdate><enddate>20240403</enddate><creator>Quan, Tingting</creator><creator>Li, Jing</creator><creator>Sun, Min</creator><creator>Chen, Yongqiang</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope></search><sort><creationdate>20240403</creationdate><title>Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension</title><author>Quan, Tingting ; Li, Jing ; Sun, Min ; Chen, Yongqiang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c314t-6a436ecb85146b953c125eb2d32be5343de5806e9eaae14474ecd3f1225297a13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Bifurcations</topic><topic>Cantilever plates</topic><topic>Coefficient of variation</topic><topic>Coordinate transformations</topic><topic>Dynamical systems</topic><topic>Fabric analysis</topic><topic>Hamiltonian functions</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Neighborhoods</topic><topic>Nonlinear systems</topic><topic>Orbits</topic><topic>Ordinary differential equations</topic><topic>Piezoelectricity</topic><topic>Poincare maps</topic><topic>Rectangular plates</topic><topic>Research Article</topic><topic>Spherical coordinates</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Quan, Tingting</creatorcontrib><creatorcontrib>Li, Jing</creatorcontrib><creatorcontrib>Sun, Min</creatorcontrib><creatorcontrib>Chen, Yongqiang</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><jtitle>Journal of nonlinear mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Quan, Tingting</au><au>Li, Jing</au><au>Sun, Min</au><au>Chen, Yongqiang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension</atitle><jtitle>Journal of nonlinear mathematical physics</jtitle><stitle>J Nonlinear Math Phys</stitle><date>2024-04-03</date><risdate>2024</risdate><volume>31</volume><issue>1</issue><spage>21</spage><pages>21-</pages><artnum>21</artnum><issn>1776-0852</issn><issn>1402-9251</issn><eissn>1776-0852</eissn><abstract>In this paper, we introduce a curvilinear coordinate transformation to study the bifurcation of periodic solutions from a 2-degree-of-freedom Hamiltonian system, when it is perturbed in
R
m
+
4
, where
m
represents any positive integer. The extended Melnikov function is obtained by constructing a Poincaré map on the curvilinear coordinate frame of the trajectory of the unperturbed system. Then the criteria for bifurcation of periodic solutions of these Hamiltonian systems under isochronous and non-isochronous conditions are obtained. As for its application, we study the number of periodic solutions of a composite piezoelectric cantilever rectangular plate system whose averaged equation can be transformed into a
(
2
+
4
)
-dimensional dynamical system. Furthermore, under the two resonance conditions of 1:1 and 1:2, we obtain the periodic solution numbers of this system with the variation of parametric excitation coefficient
p
1
.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s44198-024-00181-5</doi><oa>free_for_read</oa></addata></record> |
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| source | Springer Nature - Complete Springer Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Springer Nature OA Free Journals |
| subjects | Bifurcations Cantilever plates Coefficient of variation Coordinate transformations Dynamical systems Fabric analysis Hamiltonian functions Mathematical Physics Mathematics Mathematics and Statistics Neighborhoods Nonlinear systems Orbits Ordinary differential equations Piezoelectricity Poincare maps Rectangular plates Research Article Spherical coordinates |
| title | Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension |
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